Expert: Scotto - 5/24/2011

Question
Hello, I have a few quick questions for a homework worksheet I have to do. I believe I am doing them right but they are coming out wrong.

1. In the 6/55 lottery game, a player picks six numbers from 1 to 55. How many different choices does the player have if repetition is not allowed? Order doesn't matter.
I thought it would be 55C6 but when I typed that in my calculator and put in the answer (this is online and it tells if the answer is right or wrong) It says it's wrong but that's how we were taught so how would you go about solving that?

2. In how many ways can 3 students from a class of 22 be chosen for a field trip?
Again I did 22C3 and it didn't work.

3.  A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 5 freshmen, 8 sophomores, 8 juniors, and 9 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
This one I took the combos of each class (ie 5C2, 8C3 and so on) and then multiplied them together and it said it was wrong so I added them and it still said it was wrong.

It would be much appreciated if you could explain how I could solve these problems. Out of a set of 40, these are the only ones I could not answer.

Answer
1. The number of answers is 55*54*53*52*51*50/(6*5*4*3*2*1) = 28,989,675

2. That would be (22*21*20)/(3*2*1) = 9,240/6 = 1,540.

3. Multiplying the combos is correct.
The expressions are 5C2, 8C3, 8C4, and 9C5.
The value of these is 10, 56, 70, and 126.
The answer would be 10*56*70*126 = 4,939,200.