Question

In how many ways can a committee of three men and two women be formed from a group of eight men and seven women?

Answer 1

By counting principle rule, we have

`\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}`
`\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}`

Then the ways a committee of three men and two women can be formed is

`\binom{8}{3}\cdot\binom{7}{2}=1176`

Therefore, there are 1176 possible ways.