Homework1Solution

Homework1Solution - Homework 1 Solutions July 18, 2007 p16...

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Unformatted text preview: Homework 1 Solutions July 18, 2007 p16 21, 32 p55 15a-d, 36, 45 1. #21 Any path from A to B requires 4 moves to the right and 3 moves up, for a total of 7 steps. Of the total 7 moves, we select 4 to be right moves, and the remaining to be up moves. Therefore, the number of paths from A to B is 7 4 = 7! 3!4! = 35. 2. #32 We assume that each of the 8 people can get off the elevator at floors 1 through 6. If all people look alike, then the number of ways people can exit the elevator is equal to the number of vectors x = ( x 1 ,...,x 6 ) with ∑ 6 i =1 x i = 8. Using Proposition 6 . 2, the number of such vectors is 8+6- 1 6- 1 = 13 5 If the 8 people consisted of 5 men and 3 women and the operator could tell a man from a woman, then the number of ways people can exit the elevator is as follows. The number of vectors y multiplied by the number of vectors z where ∑ 6 i =1 y i = 5 and ∑ 6 i =1 z i = 3. Using the above argument, we have 5+6- 1 6- 1 * 3+6- 1 6- 1 = 10 5 8 5 ....
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This note was uploaded on 11/15/2008 for the course STATS 116 taught by Professor Staff during the Summer '07 term at Stanford.

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Homework1Solution - Homework 1 Solutions July 18, 2007 p16...

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