SOLUTION: from a group of 5 boys and 4 girls, a committee of 4 must be selected. Each committee must have at least one boy and at least one girl. How many ways can this be done? Thanks!

Algebra ->  Permutations -> SOLUTION: from a group of 5 boys and 4 girls, a committee of 4 must be selected. Each committee must have at least one boy and at least one girl. How many ways can this be done? Thanks!      Log On


   

Question 877118: from a group of 5 boys and 4 girls, a committee of 4 must be selected. Each committee must have at least one boy and at least one girl. How many ways can this be done?
Thanks!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The answer would be C(9,4) = 126 committees if there were no restrictions.

However we must subtract the number of committees cosisting of all boys and
the number of committees consisting of all girls.

There are C(5,4) = 5 committes of all boys.  (5 ways to leave one boy out)

There is C(4,4) = 1 committee of all girls.  (1 way to choose all 4 girls)

Answer 126 - 5 - 1 = 120 ways.

Edwin