Question

there are 5 men and 5 women to be selected to make a committee of 5 members what is the probability that all committee members are from one gender?

Answer 1

Answer on Question #47507 – Math – Statistics and Probability

Question.

There are 5 men and 5 women to be selected to make a committee of 5 members. What is the probability that all committee members are from one gender?

Solution.

$P(\text{all committee members are from one gender}) =$

$$\begin{array}{l} = P(\text{all committee members are men}) + P(\text{all committee members are women}) = \\ = \frac{C_{5}^{5}}{C_{10}^{5}} + \frac{C_{5}^{5}}{C_{10}^{5}} = 2 \cdot \frac{(5!)^{2}}{10!} = \frac{2 \cdot 2 \cdot 3 \cdot 4 \cdot 5}{6 \cdot 7 \cdot 8 \cdot 9 \cdot 10} = \frac{1}{126}. \end{array}$$

Answer: $\frac{1}{126}$

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