I need help figuring this out. It combinations and permutations.

Question

I have 2 questions on my homework I'm unable to figure out how to do and I've attempted each multiple times and have been unable to figure out the correct answer. Help figuring them out would be greatly appreciated.

1. Two coins are randomly drawn from a coin pouch. If there are 5 dimes, 2 nickels, and a quarter, how many ways can at least 20 cents be drawn out?
2.  A president, vice president, and 3 at-large members are selected for a school council from 8 people. If there is no difference between the at-large members, how many committees can be formed?

Answer 1

Mesa,

1. If you have 5 dimes, 2 nickels, and a quarter and you select 2 coins, you can get at least 20 cents if you get 2 dimes DD, a quarter and a dime QD or a quarter and a nickel, QN

DD: C(5,2) QD: C(1,1)*C(5,1) QN: C(1,1)*C(2,1)

You add up these values to get the number of ways: 10 + 5 + 2 = 17

2. There are 8 options when select the president, then 7 options to select the vice president, and there are 6 people left. From these 6 we select 3 at-large members. So the answer is

8 * 7 * C(6, 3) = 56 * 20 = 1120