i am reviewing about statistics and probability questions but i do not have answers for it and i am uncertain that my answer done well. Here is the question.

In a test, student have to answer 8 out of 10 questions . How many choices he have if he has to answer at least 3 questions at the first 5 questions?

My answer's goes like this (5C3 x 5C5) + (5C4 x 5C4) + (5C5 x 5C3) = 20 + 25 + 20 = 65 choices

My interpretation for (5C3 x 5C5) is, the student answers 3 question out of 5 first question and for the next part is 5 question answered out of the next 5 question from the second part

I want to ask does my answer valid or it might be wrong? O yeah, i also want to ask, what topics in probability covers this kind of question? Thank you so much


You are correct except that 5C3 equals 10, not 20. The total is then 45, which is exactly 10C8.

The field of study you are looking for is Combinatorics. https://en.wikipedia.org/wiki/Combinatorics

  • $\begingroup$ @r-janssen well thank you. so that's why i was wrong. I asked some friends also about this and the result is also same as yours which is 45 $\endgroup$ – user3292755 Nov 22 '15 at 17:01

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