Question

A casting director wishes to find one male and one female to cast in his play. If he plans to audition 10 males and 14 females, in how many different ways can this be done?

Answer 1

There are 10 males and 14 females.

So the order doesn't matter and we cant repeat a person.

Given the before information, we are going to use combinations

`c=(n!)/(r!(n-r)!)=`

Where n is the total of people and r the election, so:

For males:

n=10

r=1

`c=(10!)/(1!(10-1)!)=10`

For females:

n=14

r=1

`C=(14!)/(1!(14-1)!)=14`

Finally, multiply both results:

10* 14 = 140

Therefore, there are 140 ways that the casting can be done.