There are 10 males and 18 females in the Data Management class. How many different committees of 5 students can be formed if there must be 3 males and 2 femalesA: 18360B: 2600C: 98280D: 15630

Respuesta :

Answer:

A: 18360

Explanation:

The number of ways of combinations to select x people from a group of n people is calculated as

[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]

Since we need to form committees with 3 males and 2 females, we need to select 3 people from the 10 males and 2 people from the 18 females, so

[tex]10C3\times18C2=\frac{10!}{3!(10-3)!}\times\frac{18!}{2!(18-2)!}=120\times153=18360[/tex]

Therefore, there are 18360 ways to form a committee.

So, the answer is

A: 18360