Answer to Question #182301 in Statistics and Probability for Erin

Question

From a group of 7 men and 5 women a 4 person committee is chosen what is the probability that all 4 are men or all 4 are women?

Answer 1

The number of all possible events is a number of ways we can choose 4 people out of 12 which is

$C(12,4) = \begin{pmatrix} 12 \\ 4 \end{pmatrix} = 495$

The number of ways we can choose all women in the committee

$C(5,4) = \begin{pmatrix} 5 \\ 4 \end{pmatrix} = 5$

The number of ways we can choose all men in the committee

$C(7,4) = \begin{pmatrix} 5 \\ 4 \end{pmatrix} = 35$

So the probability is

$\displaystyle P(A) = \frac{5}{495} + \frac{35}{495} = \frac{40}{495}=0.08 =8\%$

Answer: 8%