Hello, cuteisa89!

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

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

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

We choose four toppings and there are only four different cheeses.c) There is only cheese on the pizza

There is onlyoneway ... choose all four of them.

Choose two vegetables from the 8 available: .C(8,2) = 28 waysd) There are 2 vegetables, 1 meat and 1 cheese

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

Choose 3 meats from the 5 meats: .C(5,3) = 10 wayse) There are 3 meats and 1 cheese.

Choose 1 cheese from the 4 cheeses: .4 ways

. . Hence: .10 x 4 .= .40 ways