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

Answer 1

Assuming the order of the answers does not matter
5C3 = 10
If the order matters
5P3 = 60

Answer 2

5•4•3
Permutation















.

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}

Answer 5

5C3 =>
5! / (3! * (5 - 3)!) =>
5 * 4 * 3! / (3! * 2!) =>
5 * 4 / 2 =>
5 * 2 =>
10