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Math Help - Kangaroo question??

  1. #1
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    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
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by hasanpak123 View Post
    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

    \underline{a},\underline{a},\underline{a},\underli  ne{a},\underline{a},\underline{b},\underline{b},\u  nderline{b},\underline{b},\underline{b}

    This is the same as asking how many ten letter words can you make with exactly 2 letters.
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  3. #3
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    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'?

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