SOLUTION: In how many ways can a mixed commitee of 5 be selected from 5 boys and 4 girls if the boys must be in the majority?

Question 728377: In how many ways can a mixed commitee of 5 be selected from 5 boys and 4 girls if the boys must be in the majority?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Case 1) If you have 5 boys on the committee, then you have 5 C 5 = 1 way to make this committee

Case 2) If you have 4 boys and 1 girl on the committee, then you have (5 C 4)*(4 C 1) = (5)*(4) = 20 ways to do this.

Case 3) If you have 3 boys and 2 girls on the committee, then you have (5 C 3)*(4 C 2) = (10)*(6) = 60 ways to do this.

You stop here because you can't have 2 boys and 3 girls. The requirement is that the boys must be in the majority, so this is why we stop here.

Add up all the results: 1+20+60 = 81

So there are 81 ways to do this.

Note: if you must have at least one girl on the committee, then there are 80 ways to do this (and you ignore case 1)
RELATED QUESTIONS
A class consists of 12 boys and 15 girls. How many different committees of four can be... (answered by ikleyn)

A teacher has 10 boys and 12 girls in her grade school class. In how many ways can she... (answered by sudhanshu_kmr)

There are 5 boys and 4 girls in a class. A committee of 5 is to be selected such that... (answered by edjones)

In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from... (answered by Edwin McCravy)

There are 5 boys and 6 girls on a grad committee In how many ways can a sub-committee... (answered by venugopalramana)

seven boys and 8 girls want to participate in a school play. In how many ways can a cast (answered by scott8148)

In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats if boys (answered by josmiceli)

in how ways can 5 boys and 3 girls be arranged in a circle if the girl must stand... (answered by greenestamps,ikleyn)

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members �be... (answered by stanbon)