You are given a 6 by 6 grid and asked to start on the top left corner. Now your aim is to get to the bottom right corner. You are only allowed to move either right or down. You must never move diagonally or backwards.

How many feasible ways are there for you to reach the end point?


this one is easy ,arrangeents of 5R and 5D i.e RRRRRDDDDD = 10!/5!5!


I don’t get this ,Can u elaborate?
Thank you


In order to reach the bottom right corner from top left corner, you have to travel through 5 rows and 5 columns. You can observe that whatever path you take, in every path you would be going through 5 rows and 5 columns.

So now say you have the rows numbered as R1 R2 R3 R4 R5
and columns numbered as C1 C2 C3 C4 C5

Now how many ways you can arrange the rows and columns so that relative ordering is maintained, i.e. R1 should be followed by R2, R2 should be followed by R3 and so on…

so it’s equal to = Total arrangements/Restricted Arrangements

= Total Arrangements/(Row Restrictions)*(Column Restrictions)