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Unformatted text preview: CSE21 FA11 Homework #1 (9/26/11) 1.1. An n-digit number is a list of n digits where the first digit in the list is not zero (where we assume n 1). (a) How many n-digit numbers are there (as a function of n )? (b) How many n-digit numbers contain no 1s? (c) How many n-digit numbers contain at least one 2? Solution: (a) There are 9 10 n- 1 n-digit numbers. (b) There are 8 9 n- 1 n-digit numbers. (c) Since there are 8 9 n- 1 n-digit numbers containing no 2s, the number of n-digits containing at least one 2s is 9 10 n- 1- 8 9 n- 1 . 1.2. In how many ways can a 10-person club select a president, a vice- president and a secretary-treasurer from among its members? What if the club has 6 men and 4 women and the three officers must consist of at least one man and at least one women? Solution: (a) The number of ways to select three officers in a 10-person club is 10 3 . (b) Since there are 6 3 ways to select three officers consisting of three men and there are 4 3 ways to select three officers consisting of three women, the number of ways to select three officers consisting of at least one man and at least one woman is 10 3- 6 3- 4 3 ....
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- Fall '07