Question

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

Answer 1

Answer:  142506

Step-by-step 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 :-

$C(n,r)=\dfrac{n!}{(n-r)!r!}$

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

$C(30,5)=\dfrac{30!}{(30-5)!5!}\\\\=\dfrac{30\times29\times28\times27\times26}{120}\\\\=142506$

Hence, the committee can be made in 142506 ways.