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

Question

Update:

Thank you very much!

Answer 1

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Assuming the order of the answers does not matter

5C3 = 10

If the order matters

5P3 = 60

Answer 2

5•4•3

Permutation

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Answer 3

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.

Answer 4

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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  Lv 4

  5 months agoReport

  excellent answer
  

Answer 5

5C3 =>

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

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

5 * 4 / 2 =>

5 * 2 =>

10