Question

A casting director wishes to find one male and one female to cast in his play. If he plans to audition 7 males and 13 females, in how many different ways can this be done?

Answer 1

From the exercise we know that there are 20 people, that 7 are men and 13 are women if only one is going to choose and one we must multiply their combinations

`C_(m,n)=(m!)/(n!(m-n)!)`

For males we have

`\begin{gathered} m=7 \\ n=1 \\ C_{\text{male}}=(7!)/(1!(7-1)!) \\ C_{\text{male}}=7 \\ \end{gathered}`

For females we have

`\begin{gathered} m=13 \\ n=1 \\ C_{\text{female}}=(13!)/(1!(13-1)!) \\ C_{\text{female}}=13 \end{gathered}`

Now we multiply the combinations to know how many options the director has to choose his actors

`\begin{gathered} C_{\text{male}}\cdot C_{\text{female}}=7\cdot13 \\ C_{\text{male}}\cdot C_{\text{female}}=91 \end{gathered}`

The answer is there are 91 ways to audition.