In how many ways can a commitee of 4 people be drawn from a group of 13 people?

Expert Answers
justaguide eNotes educator| Certified Educator

When a committee of 4 has to be formed from a group of 13 people, the order in which they are selected does not make a difference. The number of ways in which the committee can be formed can be determined using combinations.

As the 4 members are chosen from a group of 13, the number of ways is C(13, 4)

`C(13, 4) = (13!)/(9!) = 13*12*11*10 = 17160`

There are 17160 ways in which the committee can be formed.

nmmoritz eNotes educator| Certified Educator

In the first position, 13 people are possible to be chosen.

Then, in the second position, only 12 are available because one of them has already been chosen for the first spot.

For the third position, 11 people are available, and in the last position, only 10 are available.

Therefore, 

13 x 12 x 11 x 10 = 17,160 possibilities