6.In how many ways can one travel from (0,0) to (8,11) going only
East or North, and while passing through (4,7) ?
Anyone knows how to do this one?
Answer: try splitting it up to (0, 0) to (4, 7) and then (4, 7) to (8, 11)
Yes, you should spilt up the problem in two parts. The first part there are 11 total ways to get to the final product: 4 steps to the right, 7 steps up. Therefore, we get 11!/(4!*7!). For the second part, there are 8 total ways to get the final product:4 steps to the right and 4 steps up. Therefore, we get 8!/(4!4!). The answer to the first part is 330 which we multiply with the second answer, which is 70.
11!/(4!*7!) * 8!/(4!4!) = 330 * 70 = 23100 ways total. I believe this is correct. - Carolyn Hanes --Chanes 00:21, 12 March 2012 (UTC)
