Guided Example #2 - Factorials, Combination, Permutation

In a company there are seven executives: four women and three men. Three are selected to attend a seminar. Find the probability that one man and two women will be selected.

A. $\frac{3}{35}$ B. $\frac{6}{35}$ C. $\frac{18}{35}$ D. $\frac{12}{35}$

Step 1

Let's start by finding the sample space. There are seven people and we are picking 3 of them.
This can be done in
$C_{3}^{7} = 7 \frac{!}{(3!) (4!)} = 35$ ways.

There are 3 ways to pick one man out of $3 (C_{1}^{3} = 3)$ and 6 ways $(C_{2}^{4} = 6)$ to pick 2 women out of 4.
So the desired probability is
$P = \frac{C_{1}^{3} C_{2}^{4}}{C_{3}^{7}} = \frac{(3) (6)}{35} = \frac{18}{35}$ .

All Steps

Let's start by finding the sample space. There are seven people and we are picking 3 of them.
This can be done in
$C_{3}^{7} = 7 \frac{!}{(3!) (4!)} = 35$ ways.

Guided Example #2 - Factorials, Combination, Permutation

Step 1

Step 2

All Steps