Question

Three student representatives, a president, a secretary, and a treasurer, are to be chosen from a group of five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be menNote that Brenda and Dorothy are women while Andrew, Chad, and Eric are men

Answer 1

Answer:

Number of ways that the representative can be chosen = 12

Explanation:

The number of women = 2

The number of men = 3

Since the president must be a woman

Number of ways of choosing the president = 2C1

$\begin{gathered} 2C1=\text{ }\frac{2!}{(2-1)!1!} \\ 2C1=2 \end{gathered}$

Number of ways of choosing the president = 2

The secretary and treasurer must be men

Let us first choose the secretary out of all the three men

Number of ways of choosing the secretary = 3C1

$\begin{gathered} 3C1=\text{ }\frac{3!}{(3-1)!1!} \\ 3C1=\text{ }\frac{3!}{2!} \\ 3C1\text{ = }\frac{3\times2\times1}{2\times1} \\ 3C1=\text{ 3} \end{gathered}$

Number of ways of choosing the secretary = 3

After the secretary has been selected, there are 2 men left

Number of ways of selecting the treasurer = 2C1

Number of ways of choosing the treasurer = 2

Number of ways that the representative can be chosen = 2 x 3 x 2

Number of ways that the representative can be chosen = 12