SOLUTION: A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be

Algebra ->  Permutations -> SOLUTION: A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be       Log On


   

Question 945376: A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be accountant?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be accountant?
There are 3 accountants and 9 non-accountants.

Case 1. Choose 2 accountants, 3 non-accountants

Choose the 2 accountants 3C2 = 3 ways.
Choose the 3 non-accountants 9C3 = 84
That's 3*84 = 252 ways.

Case 1.  Choose all 3 accountants, 2 non-accountants

Choose all 3 accountants 3C3 = 1 way.
Choose the 2 non-accountants 9C2 = 36
That's 1*36 = 36 ways.

Grand total: 252+36 = 288

Edwin