Permutations and Combinations

1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?

2. 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?

3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?

4. 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

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.

What's your favorite combo?