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)
