A company that has 250 employees chooses a committee of 18 to represent employee

Question

A company that has 250 employees chooses a committee of 18 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use technology to find the number of ways 18 employees can be chosen from 250. (b) Use technology to find the number of ways 18 employees can be chosen from194 nonminorities. (c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)? (d) Does your answer to (c) indicate that the committee selection is biased? Explain your reasoning.

Explanation / Answer

a)

number of ways of choosing 18 employees from 250

= 250C18

= 1.2144 * 10^27

b)

number of ways of choosing 18 employees from 194

= 194C18

= 1.049 * 10^25

c)

probability = 1.049 * 10^25/1.2144 * 10^27

= 0.0086

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