Math Help - Kangaroo question??

26. A test is composed of ten questions each of which must be answered “a” or “b”. If you answer
any 5 questions „a” and any 5 questions „b”, the number of correct answers is guaranteed to be
at least 4. How many answer keys are there with this property?
A) 5^5 B) 252 C) 2 D) 10 E) 22

Originally Posted by hasanpak123

26. A test is composed of ten questions each of which must be answered “a” or “b”. If you answer
any 5 questions „a” and any 5 questions „b”, the number of correct answers is guaranteed to be
at least 4. How many answer keys are there with this property?
A) 5^5 B) 252 C) 2 D) 10 E) 22

I will answer your question with a question.

How many distinguishable permutations are there of



This is the same as asking how many ten letter words can you make with exactly 2 letters.

10!/5!*5!

Thats 252...What about the 4... Is it just to confuse us? By 'answer key', do they mean the number of solutions we can derive answering each answer 'a' or 'b'?

Thanks