Homework Help

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

user profile pic

utilityfan | Student, College Freshman

Posted May 25, 2012 at 2:34 PM via web

dislike 2 like

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

2 Answers | Add Yours

user profile pic

nmmoritz | Middle School Teacher | (Level 1) Adjunct Educator

Posted May 25, 2012 at 2:40 PM (Answer #1)

dislike 1 like

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

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 25, 2012 at 2:56 PM (Answer #2)

dislike 1 like

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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes