# Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3: 56

4

#### 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 a female professor can be chosen when there are four female professors. = 4C3 x 1! =$\frac{4!}{(4-3)!3!}$ =$\frac{4*3!}{3!1!}$ =$\frac{4}{1}$ = 4 ways

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