MCQ Test design

Question

Stumped with this problem:

20 question multiple choice test with answer options A - E.

How many designs exist that contain 2 A, 3 B, 9 C, 4 D and 2 E as correct answers?

It appears that this should be an unordered set and combinations should be used, but I can't figure out how to put the 5 subsets together to make this work.

Any thoughts?

Answer 1

Think of the answers as a single word containing the letters AABBBCCCCCCCCCDDDDEE

20!

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2! 3! 9! 4! 2!