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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

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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

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  • $\begingroup$ @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, 2015 at 17:01

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