# Combinations Help

• Mar 14th 2007, 02:15 PM
cuteisa89
Combinations Help
Hi, I'm stuck in these two problems. Can somebody help me? Thanks.

1. I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?

2. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses.
How many ways can 4 toppings be selected where:

a) All the toppings are vegetables. (I think this one is 70)
b) All the toppings are meat.
c) There is only cheese on the pizza
d) There are 2 vegetables, 1 meat and 1 cheese
e) There are 3 meats and 1 cheese.
• Mar 14th 2007, 02:58 PM
Soroban
Hello, cuteisa89!

Quote:

1. I've decided that the mentor group should be made up of 3 girls and 3 boys.
Of the students who have A's 9 of them are girls and 6 are boys.
How many ways can I form a group of 3 boys and 3 girls?

To select the three girls, there are: C(9,3) = 84 ways.
To select the three boys, there are: C(6,3) = 20 ways.

Therefore, there are: .84 x 20 .= .1680 ways to choose the mentor group.

Quote:

2. A pizza shop offers the following toppings: 8 different vegetables,
5 different meats, and 4 different cheeses.

How many ways can 4 toppings be selected where:

a) All the toppings are vegetables. (I think this one is 70) Yes!

b) All the toppings are meat.

Choose 4 of the 5 meats: .C(5,4) = 5 ways.

Quote:

c) There is only cheese on the pizza
We choose four toppings and there are only four different cheeses.
There is only one way ... choose all four of them.

Quote:

d) There are 2 vegetables, 1 meat and 1 cheese
Choose two vegetables from the 8 available: .C(8,2) = 28 ways
Choose one meat from the 5 meats: .5 ways
Choose one cheese from the 4 cheeses: .4 ways
. . Hence: .28 x 5 x 4 .= .560 ways

Quote:

e) There are 3 meats and 1 cheese.
Choose 3 meats from the 5 meats: .C(5,3) = 10 ways
Choose 1 cheese from the 4 cheeses: .4 ways
. . Hence: .10 x 4 .= .40 ways