SOLUTION: From a group of 6 girls and 7 boys, how many 5-member committees consist of : more boys than girls? Multiple choice answers: a. 534 b. 656 c. 256 d. 756

Algebra ->  Permutations -> SOLUTION: From a group of 6 girls and 7 boys, how many 5-member committees consist of : more boys than girls? Multiple choice answers: a. 534 b. 656 c. 256 d. 756      Log On


   

Question 1161679: From a group of 6 girls and 7 boys, how many 5-member committees consist of :
more boys than girls?
Multiple choice answers:
a. 534
b. 656
c. 256
d. 756
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


There are three scenarios to consider ( C(n,r) = n!/((n-r)!r!) ):

1. You can choose 3 boys and 2 girls:  C(7,3)*C(6,2)

2. You can choose 4 boys and 1 girl:  C(7,4)*C(6,1)

3. You can choose 5 boys and 0 girls:  C(7,5)*C(6,0)



Calculate each result and add them (they are mutually exclusive, so you can add them without overcounting).