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| + | [[Category:discrete math]] | ||
| + | [[Category:lecture notes]] | ||
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| + | =[[MA375]]: Practice Questions= | ||
| + | Spring 2012, Prof. Walther | ||
| + | ---- | ||
6.In how many ways can one travel from (0,0) to (8,11) going only | 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) ? | East or North, and while passing through (4,7) ? | ||
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Answer: try splitting it up to (0, 0) to (4, 7) and then (4, 7) to (8, 11) | 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. | + | - 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!). | 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!). | 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. | 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. | + | 11!/(4!*7!) * 8!/(4!4!) |
| + | = 330 * 70 | ||
| + | = 23100 ways total. | ||
| + | |||
I believe this is correct. - Carolyn Hanes --[[User:Chanes|Chanes]] 00:21, 12 March 2012 (UTC) | I believe this is correct. - Carolyn Hanes --[[User:Chanes|Chanes]] 00:21, 12 March 2012 (UTC) | ||
| + | ---- | ||
| + | [[2012_Spring_MA_375_Walther|Back to MA375 Spring 2012 Prof. Walther]] | ||
Latest revision as of 09:42, 20 May 2013
MA375: Practice Questions
Spring 2012, Prof. Walther
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)
