SOLUTION: Please help i am kinda confused.' 5. At Grant senior high school, there are 15 names on the ballot for the junior class officers.Five will be selected to form a class committee?

Question 1081075: Please help i am kinda confused.'
5. At Grant senior high school, there are 15 names on the ballot for the junior class officers.Five will be selected to form a class committee?
c. If there are 8 girls and 7 boys on the ballot, how many committee of boys and 3 girls can be formed?

Found 3 solutions by Boreal, MathLover1, jorel1380:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
2 boys and 3 girls I assume is the committee
8C3 girls (56)
7C2 boys (21)
They are independent of each other, so the product is 1176 ways.
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

a.
How many different committees of can be formed?
Order is not important in this situation, so the selection is a combination of
people chosen at a time.

There are different ways to form the committees of .

b.
Order has to be considered in this situation because each committee
member has a different responsibility.

There are possible committees.

c.
Order is not important. There are three questions to consider.
How many ways can boys be chosen from ?
How many ways can girls be chosen from ?
Then, how many ways can boys and girls be chosen together?
Since the events are independent, the answer is the product of the combinations
and .

There are possible committees.

Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
15 choose 5=3003 possible committees.
Out of a committee of 5,there are 2 boys, and 3 girls. So 7 choose 2 boys x 8 choose 3 girls equals 21 x 56=1176 different committees. ☺☺☺☺

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