# Probability problem!

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A group of 10 students includes 3 from Year 12 and four from Year 11. The principal calls a meeting with 5 students randomly selected from the group. Calculate the probability that exactly 2 Year 12 and 2 Year 11 students are called to the meeting.

ANS: 3/14

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This is a nonsensical question ... there are only 4 students called to the meeting when you need 5.

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@kw0573 yeah so it means that there are 3 students with other grade levels.

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This is called a hypergeometric distribution, but you don't have to know the term. If you are interested you can look it up.

Denote (n, k) as the binomial coefficient, n choose k, (n, k) = n! / (k! * (n-k)!). Combination because the students show up together, not because the students are non-distinct.

The answer is (3, 2) * (4, 2) * (3, 1) / (10, 5). which is combinations of 2 grade 12s * combinations of 2 grade 11s, * combinations of 1 student from another grade, divided by all combinations of 5 students from a group of 10.

Note that when we are given the number of students in each grade, the combinations of one grade is independent from combinations of another grade, so we can multiply these possibilities together, then finally divided by the total possibility of choosing 5 students.
You get 3 * 6 * 3 / 252 = 3/14

Edited by kw0573
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