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# Combination Probability

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There are 3 math clubs in the school district, with 5, 7, and 8 students respectively. Each club has two co-presidents. If I randomly select a club, and then randomly select three members of that club to give a copy of Introduction to Counting and Probability, what is the probability that two of the people who receive books are co-presidents?

On numerous occasions, I have seen answers without work and have inputted them, and they are wrong most of the time. If you do not show work, I will not be using your answer.

Apr 4, 2021

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Introduction to counting and probability is a great book ;)

Let's first calculate the probability for each club then average them.

5 student club - There are $\binom{5}{3}=10$ ways to choose the members. In $\binom{2}{2}\binom{3}{1}=3$ ways, the co-presidents are selected - the probability here is $\frac{3}{10}$.

7 student and 8 student clubs are analogous. Try it, I believe in you!

Apr 4, 2021
edited by thedudemanguyperson  Apr 4, 2021
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Thank you for your solution! I finished the problem for 7 and 8 students, and got $\frac{11}{60}$, which was correct! Thanks again, this helped me a lot!

RiemannIntegralzzz  Apr 4, 2021
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No problem, keep the good work up! I hope to see you soon on the Alcumus hall of fame (or if it's a homework problem, on the forums).