Hello everyone, I am looking for some help with the following math problem.

A dorm floor consisting of 20 people wish to make up a hockey team.

a) In how many ways can you choose 12 people from the 20 people on your dorm floor to make up a hockey team?

* I think for this question I should use combinations -20C12 = 125,970 ways. However please correct me if I am wrong.

b) For the first name, you must assign 6 out of the 12 people on your team to be forwards, 4 to be defense and 2 to be a goalie. In how many ways can you do this?

Would it be 12C6* 6C4 * 2C2 = 13,860 WAYS?

C) The team decides they want 4 captains with at least one of the captains being a goalie.How many ways can a group of 4 captains with at least one goalie be drawn?

I am not sure how to approach this one.

Thank you!!!!

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