## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3: 57

60

#### Work Step by Step

The number of possible combinations if r items are taken from n items is nCr =$\frac{n!}{r!(n-r)!}$ We find the number of ways that two Democrats can be chosen from four candidates and two Republicans can be chosen from 5 candidates. =4C2 x 5C2 = $\frac{4!}{2!(4-2)!}$ x $\frac{5!}{2!(5-2)!}$ =$\frac{4*3*2!}{2!2!}$ x $\frac{5*4*3!}{2!3!}$ =$\frac{4*3}{2*1}$ x $\frac{5*4}{2*1}$ =6 x 10 =60 ways

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