Street Combinatorics - 6 by 7 grid

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
3
down vote

favorite
1












You go to school in a building located six blocks east and seven blocks north
of your home. So, in walking to school each day you go thirteen blocks. All streets in a rectangular pattern are available to you for walking.
In how many different paths can you go from home to school, walking only thirteen
blocks?



I want to say that the answer can be found knowing that there are $6!$ ways east and $7!$ ways north. Then, the answer would be $6!+ 7!$ .



I feel like this is way too simple of a solution to be correct.






combinatorics







share|cite|improve this question







New contributor




Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.























    up vote
    3
    down vote

    favorite
    1












    You go to school in a building located six blocks east and seven blocks north
    of your home. So, in walking to school each day you go thirteen blocks. All streets in a rectangular pattern are available to you for walking.
    In how many different paths can you go from home to school, walking only thirteen
    blocks?



    I want to say that the answer can be found knowing that there are $6!$ ways east and $7!$ ways north. Then, the answer would be $6!+ 7!$ .



    I feel like this is way too simple of a solution to be correct.






    combinatorics







    share|cite|improve this question







    New contributor




    Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.





















      up vote
      3
      down vote

      favorite
      1









      up vote
      3
      down vote

      favorite
      1






      1





      You go to school in a building located six blocks east and seven blocks north
      of your home. So, in walking to school each day you go thirteen blocks. All streets in a rectangular pattern are available to you for walking.
      In how many different paths can you go from home to school, walking only thirteen
      blocks?



      I want to say that the answer can be found knowing that there are $6!$ ways east and $7!$ ways north. Then, the answer would be $6!+ 7!$ .



      I feel like this is way too simple of a solution to be correct.






      combinatorics







      share|cite|improve this question







      New contributor




      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      You go to school in a building located six blocks east and seven blocks north
      of your home. So, in walking to school each day you go thirteen blocks. All streets in a rectangular pattern are available to you for walking.
      In how many different paths can you go from home to school, walking only thirteen
      blocks?



      I want to say that the answer can be found knowing that there are $6!$ ways east and $7!$ ways north. Then, the answer would be $6!+ 7!$ .



      I feel like this is way too simple of a solution to be correct.






      combinatorics




      combinatorics






      share|cite|improve this question







      New contributor




      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question







      New contributor




      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question






      New contributor




      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 1 hour ago









      Ludwigthestud

      262




      262




      New contributor




      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Ludwigthestud is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.




















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          4
          down vote













          Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.



          This is equivalent to the problem



          nnnnnnneeeeee


          How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $$13choose6=frac13!6!7!=colorred1716$$






          share|cite|improve this answer



























            up vote
            3
            down vote













            Consider this:



            You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?



            The answer is then $binom6+76=binom136=1716$






            share|cite|improve this answer






















            • I think you messed up the combination notation...
              – Rushabh Mehta
              1 hour ago










            • @RushabhMehta I did. Thank you for point it out.
              – abc...
              1 hour ago










            Your Answer




            StackExchange.ifUsing("editor", function ()
            return StackExchange.using("mathjaxEditing", function ()
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            );
            );
            , "mathjax-editing");

            StackExchange.ready(function()
            var channelOptions =
            tags: "".split(" "),
            id: "69"
            ;
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function()
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled)
            StackExchange.using("snippets", function()
            createEditor();
            );

            else
            createEditor();

            );

            function createEditor()
            StackExchange.prepareEditor(
            heartbeatType: 'answer',
            convertImagesToLinks: true,
            noModals: false,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            );



            );






            Ludwigthestud is a new contributor. Be nice, and check out our Code of Conduct.









             

            draft saved


            draft discarded


















            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2917360%2fstreet-combinatorics-6-by-7-grid%23new-answer', 'question_page');

            );

            Post as a guest

















            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            4
            down vote













            Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.



            This is equivalent to the problem



            nnnnnnneeeeee


            How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $$13choose6=frac13!6!7!=colorred1716$$






            share|cite|improve this answer
























              up vote
              4
              down vote













              Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.



              This is equivalent to the problem



              nnnnnnneeeeee


              How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $$13choose6=frac13!6!7!=colorred1716$$






              share|cite|improve this answer






















                up vote
                4
                down vote










                up vote
                4
                down vote









                Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.



                This is equivalent to the problem



                nnnnnnneeeeee


                How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $$13choose6=frac13!6!7!=colorred1716$$






                share|cite|improve this answer












                Let's assume the only moves you are allowed are moving north and moving east. Denote a move north as n and a move east as e. Hence, we need to make 7 n moves and 6 e moves, and we seek to compute the number of arrangements of these moves.



                This is equivalent to the problem



                nnnnnnneeeeee


                How many distinct rearrangements are there of the above letters. Through some combinatorics, we find the answer is $$13choose6=frac13!6!7!=colorred1716$$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 1 hour ago









                Rushabh Mehta

                2,178221




                2,178221




















                    up vote
                    3
                    down vote













                    Consider this:



                    You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?



                    The answer is then $binom6+76=binom136=1716$






                    share|cite|improve this answer






















                    • I think you messed up the combination notation...
                      – Rushabh Mehta
                      1 hour ago










                    • @RushabhMehta I did. Thank you for point it out.
                      – abc...
                      1 hour ago














                    up vote
                    3
                    down vote













                    Consider this:



                    You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?



                    The answer is then $binom6+76=binom136=1716$






                    share|cite|improve this answer






















                    • I think you messed up the combination notation...
                      – Rushabh Mehta
                      1 hour ago










                    • @RushabhMehta I did. Thank you for point it out.
                      – abc...
                      1 hour ago












                    up vote
                    3
                    down vote










                    up vote
                    3
                    down vote









                    Consider this:



                    You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?



                    The answer is then $binom6+76=binom136=1716$






                    share|cite|improve this answer














                    Consider this:



                    You have to go north 7 times and go east 6 times. How can you slip in the 6 "east moves" into 7 "north moves"?



                    The answer is then $binom6+76=binom136=1716$







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited 1 hour ago

























                    answered 1 hour ago









                    abc...

                    1,897527




                    1,897527











                    • I think you messed up the combination notation...
                      – Rushabh Mehta
                      1 hour ago










                    • @RushabhMehta I did. Thank you for point it out.
                      – abc...
                      1 hour ago
















                    • I think you messed up the combination notation...
                      – Rushabh Mehta
                      1 hour ago










                    • @RushabhMehta I did. Thank you for point it out.
                      – abc...
                      1 hour ago















                    I think you messed up the combination notation...
                    – Rushabh Mehta
                    1 hour ago




                    I think you messed up the combination notation...
                    – Rushabh Mehta
                    1 hour ago












                    @RushabhMehta I did. Thank you for point it out.
                    – abc...
                    1 hour ago




                    @RushabhMehta I did. Thank you for point it out.
                    – abc...
                    1 hour ago










                    Ludwigthestud is a new contributor. Be nice, and check out our Code of Conduct.









                     

                    draft saved


                    draft discarded


















                    Ludwigthestud is a new contributor. Be nice, and check out our Code of Conduct.












                    Ludwigthestud is a new contributor. Be nice, and check out our Code of Conduct.











                    Ludwigthestud is a new contributor. Be nice, and check out our Code of Conduct.













                     


                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2917360%2fstreet-combinatorics-6-by-7-grid%23new-answer', 'question_page');

                    );

                    Post as a guest
































































                    Comments

                    Post a Comment

                    Popular posts from this blog

                    Long meetings (6-7 hours a day): Being “babysat” by supervisor

                    Image
                    Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 31 down vote favorite 4 I hold a PhD in mechanical engineering with a 7 year background in self-guided, self-paced research including 2 years as a graduate level course instructor and a subject matter expert for various engineering projects in a university setting in the United States. For the last 10-11 months, I am working in a research industry in France where my task is to debug C++ spaghetti code written over a period of several years by my current supervisor. It is a team of 2: just I and my supervisor. Diurnally, I am posed with a "bug of the day" to get out of this C++ code. My supervisor generally gives me about 15-30 minutes to solve it and then accosts me about whether or not the task is completed and then rinses and repeats this until the end of the day. Off-late, my supervisor has been holding 6-7 hour long "meetin
                    Read more

                    Is the Concept of Multiple Fantasy Races Scientifically Flawed? [closed]

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite Many fantasy worlds have multiple humanoid species (elves, orcs, humans, etc) living in the same world, in addition to that, they often have the ability to interbreed. And I can't help but question their believability... fantasy-races reproduction interspecies-relations share | improve this question edited Aug 9 at 14:46 Michael Kjörling ♦ 21.1k 10 85 161 asked Aug 9 at 13:13 Chlodio 118 6 closed as unclear what you're asking by MichaelK, Gryphon, John, Vincent, Frostfyre Aug 9 at 15:25 Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. 3 Stack Exchange exist to
                    Read more

                    Confectionery

                    Image
                    Prepared foods made with a lot of sugar or other cabohydrates "Sweetmeat" redirects here. For the racehorse, see Sweetmeat (horse). Not to be confused with Sweetbread. This Kransekake is a traditional Scandinavian baker's confection. Confectionery is the art of making confections , which are food items that are rich in sugar and carbohydrates. Exact definitions are difficult. [1] In general, though, confectionery is divided into two broad and somewhat overlapping categories, bakers' confections and sugar confections. [2] Bakers' confectionery, also called flour confections , includes principally sweet pastries, cakes, and similar baked goods. Sugar confectionery includes candies ( sweets in British English), candied nuts, chocolates, chewing gum, bubble gum, pastillage, and other confections that are made primarily of sugar. In some cases, chocolate confections (confections made of chocolate) are treated as a separate category, as are sugar-free versions of
                    Read more