Solution1

# Solution1 - SOLUTIONS FOR HOMEWORK 1 1 This can be solved...

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SOLUTIONS FOR HOMEWORK 1 1. This can be solved by the generalized counting principle. (a) 26 × 10 × 10 × 10 × 10 × 10 = 67 , 600 , 000. (b) 26 × 25 × 10 × 9 × 8 × 7 × 6 = 19 , 656 , 000. 7. (a) Since there are 6 people intotal, there are 6! = 720 permutations. (b) It consists of three steps. The ﬁrst step is to divide the seats into two parts, one for boys and the other for girls, there are 2 ways for this arrangement. The second step is to permute 3 boys among themselves, there are 3! ways. The last step is to permute 3 girls among themselves, there are 3! ways. By the generalized counting principle, there are 2 · 3! · 3! = 72 ways. (c) First we regard the 3 boys as one person, so together with 3 girls we have 4 persons, there are 4! ways to permute these 4 persons. Then we permute the 3 boys among themselves, there are 3! ways. By the counting principle there are 4! · 3! = 144 ways in total. (d) First there are 3! ways to arrange the girls. Since two people

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## This note was uploaded on 04/13/2008 for the course M 362k taught by Professor Berg during the Spring '08 term at University of Texas.

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Solution1 - SOLUTIONS FOR HOMEWORK 1 1 This can be solved...

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