Respuesta :
Answer:
155 ways are there to select the committee that has more women than men.
Step-by-step explanation:
The order is not important.
For examle, a committee of John, Elisa, Josh and Rose is the same committee as Elisa, John, Josh and Rose. So we use the combinations formula to solve this problem.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many ways are there to select the committee that has more women than men?
It can either be 3 women and a men, or 4 women.
3 women and a men
1 men from a set of 15
3 women from a set of 5
[tex]C_{5,3}*C_{15,1} = \frac{5!}{3!(2)!}*\frac{15!}{1!(14)!} = 150[/tex]
4 women
4 women from a set of 5
[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]
Total
150 + 5 = 155
155 ways are there to select the committee that has more women than men.
