# Targeting topics to revise: risk of coming unstuck

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Hi guys - been a while since I did combinations and permutations so just wanted to check something.

The question is about the risk involved with revising fewer topics on a university module where you have to do a set number of essay questions from a list.

Example: There are 10 topics on the course. The exam has 6 questions of which you have to answer 3. Assume each topic has an equal chance of coming up in the 6 and no topics will have more than one question in the exam.

My thoughts are:

- revising 7 or more topics will guarantee you can answer 3 questions, as even if all of the ones you don't revise come up in the 6, that will leave 3 that you can answer.

- revising 6 topics means there is a (6C2 x 4C4)/(10C6) = 1 in 14 chance (7.14%) that you will be in a position where fewer than 3 questions that you have revised come up on the paper.

- revising 5 topics means there is a (5C2 x 5C4)/10C6 + (5C1 x 5C5)/10C6 = 11 in 42 chance (26.19%) that you will be in a position where fewer than 3 questions you have revised come up.

- revising 4 topics means there is a (4C2 x 6C4)/10C6 + (4C1 x 6C5)/10C6 + 6C6/10C6 = 23 in 42 chance (54.76%) that you will be screwed.

- revising 3 topics (LOL) means there is a (1 - 3C3/10C6) = 209 in 210 chance (99.52%) that you will be screwed.

Is this accurate or have I done something wrong?

(note - I'm not actually doing an exam, but this question came up with me and some of my friends who are, and so I was trying to think of how to assess the risk through using combinations but am a bit rusty!)
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