We need to select 3 of the 8 people. Since the order of the people is not important (as a different order results in the same people being selected), we need to use a combination.

Definition combination (order is not important);\(nCr=(n r)=\frac{n!}{r!(n-r)!}\) with \(n!=n(n-1) \cdot \ldots \cdot 2 \cdot 1\). # of possible outcomes=\(sC_3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!5!}=56\)

We need to select 2 of the 5 women and 1 of the 3 men to obtain \(X=2\). # of favorable outcomes=\((5C_2 \cdot 3)C_1=(\frac{5!}{2!3!}) \cdot \frac{3!}{1!2!}=10 \cdot 3=30\)

The probability is the number of favorable outcomes divided by the number of possible outcomes: \(Pr(X=2)=\)\(\frac{\text{# of favorable outcomes}}{\text{ # of possible outcomes}}\) \(=\frac{30}{56} =\frac{15}{28}\) \(~ 0.5357 =53.57\%\)