Students in a maths test can score 0, 1, 2 or 3 marks on each of the six questions. There is only one way to score 18 and six ways to score 17. In how many ways can a student score 16?

There is only one way to score an 18, because all the questions need to score a three, but with 17, any of the questions can score a 2, but only one, the rest must still score a three. there are six ways because there are six questions. it is only a matter of choosing which one. Similarly with 16, but a little more complicated. the ways to get a 16 are, get a two on two questions, or get a one on one question. the ways to get a one are the same as the ways in getting 17, six ways. the ways to get a two on two is to take the six questions and choose the two that receive a two. that is 6 choose 2, or 15 ways so, a student can get a 16 on the test 15+6=21 ways.

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