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| + | [[Category:MA375]] | ||
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| + | =[[MA375]]: Lecture Notes= | ||
| + | Fall 2008, Prof. Walther | ||
| + | ---- | ||
| + | ==Midterm Review== | ||
Sample question.<br> | Sample question.<br> | ||
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)?<br><br> | 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)?<br><br> | ||
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3) By product rule (you can pair up each way from 1) with a way from 2) ) total number of ways to go from (0,0) to (8,11) through (4,7) is (11 choose 4) * (8 choose 4) = 23100<br> | 3) By product rule (you can pair up each way from 1) with a way from 2) ) total number of ways to go from (0,0) to (8,11) through (4,7) is (11 choose 4) * (8 choose 4) = 23100<br> | ||
--[[User:Asuleime|Asuleime]] 15:59, 26 October 2008 (UTC) | --[[User:Asuleime|Asuleime]] 15:59, 26 October 2008 (UTC) | ||
| + | ---- | ||
| + | [[Main_Page_MA375Fall2008walther|Back to MA375, Fall 2008, Prof. Walther]] | ||
Latest revision as of 08:15, 20 May 2013
MA375: Lecture Notes
Fall 2008, Prof. Walther
Midterm Review
Sample question.
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)?
Solution
1) There are (11 choose 4) ways to go from (0,0) to (4,7). The explanation: you have to do 11 moves, 4 of them should be east (alternatively 7 of them should be north).
2) There are (((8-4)+(11-7)) choose (8-4))=(8 choose 4) ways to go from (4,7) to (8,11). The explanation: you have to do 8 moves, 4 of them should be east (alternatively 4 of them should be north).
3) By product rule (you can pair up each way from 1) with a way from 2) ) total number of ways to go from (0,0) to (8,11) through (4,7) is (11 choose 4) * (8 choose 4) = 23100
--Asuleime 15:59, 26 October 2008 (UTC)
