In how many different ways can a five-question test be answered, if only three of them have to be answered?
Thank you very much!
5 Answers
- Mike GLv 75 months agoFavorite Answer
Assuming the order of the answers does not matter
5C3 = 10
If the order matters
5P3 = 60
- Anonymous5 months ago
5•4•3
Permutation
.
- LeonardLv 75 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.
- PuzzlingLv 75 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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- 5 months ago
5C3 =>
5! / (3! * (5 - 3)!) =>
5 * 4 * 3! / (3! * 2!) =>
5 * 4 / 2 =>
5 * 2 =>
10
excellent answer