In how many different ways can a five-question test be answered, if only three of them have to be answered?

Update:

Thank you very much!

5 Answers

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  • Mike G
    Lv 7
    5 months ago
    Favorite Answer

    Assuming the order of the answers does not matter

    5C3 = 10

    If the order matters

    5P3 = 60

  • Anonymous
    5 months ago

    5•4•3

    Permutation

    .

  • 5 months ago

    The question is very unclear - first, even if you mean counting whether a question was answered or not, "if only 3 of them HAVE TO to be answered" - does this mean answering exactly 3 questions and leaving the others blank, or can you answer either 3 or 4 or all 5 questions - you'll get different responses to your question depending.

    Also, are the questions "multiple choice"? if yes, then every question can be answered in 4 ways (each of the 4 choices), or it can be left blank and not answered at all.

    You have to ask your question precisely, or it cant be answered precisely.

  • 5 months ago

    Assuming they pick the 3 questions they are going to answer, it's simply "5 choose 3".

    5C3 = (5 * 4 * 3) / (3 * 2 * 1)

    = 60/6

    = 10 ways

    Specifically:

    {123, 124, 125, 134, 135, 145, 234, 235, 245, 345}

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  • 5C3 =>

    5! / (3! * (5 - 3)!) =>

    5 * 4 * 3! / (3! * 2!) =>

    5 * 4 / 2 =>

    5 * 2 =>

    10

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