# 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!

Relevance

Assuming the order of the answers does not matter

5C3 = 10

If the order matters

5P3 = 60

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• Anonymous
6 months ago

5•4•3

Permutation

.

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• 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.

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• 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}

• Lv 4
6 months agoReport

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• 5C3 =>

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

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

5 * 4 / 2 =>

5 * 2 =>

10

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