Question

A casting director wishes to find one male and one female to cast in his play. If he plans to audition 12 males and 12 females, in how many different ways can this be done?

Answer 1

Given:

The number of males = 12

The number of females = 12

The number of ways to select r objects from n objects is given as,

`^nC_r=(n!)/(r!(n-r)!)`

The number of ways to choose one male and one female is given as,

`\begin{gathered} \text{Number of ways=}^(12)C_1*^(12)C_1 \\ =(12!)/(1!(12-1)!)*(12!)/(1!(12-1)!) \\ =12*12 \\ =144 \end{gathered}`

Answer: the numbers of ways are 144.