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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online