Hello, cuteisa89!

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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.

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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.

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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.

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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

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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