+487 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?
PLEASE SHOW WORK OR I WILL NOT BE USING YOUR ANSWER!!!
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.
+605 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!
+487 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!
+605 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).
