Question

In how many ways can a committee of 5 people be chosen from a total of 30 possible people?

Answer 1

Answer: 142506

Explanation:

Given : The total number of choices for people in committee = 30

The number of people need to be chosen =5

Since , here order doesn't matter, so we use combination.

The combination of r things taking from n at a time is given by :-

`C(n,r)=(n!)/((n-r)!r!)`

Now, the number of possible combinations of 5 people be chosen from a total of 30 possible people :-

`C(30,5)=(30!)/((30-5)!5!)\\\\=(30*29*28*27*26)/(120)\\\\=142506`

Hence, the committee can be made in 142506 ways.