Exercise 1.55

Question

A club consists of 10 seniors, 12 juniors, and 15 sophomores. An organizing committee of size 5 is chosen randomly (with all subsets of size 5 equally likely).
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(a) Find the probability that there are exactly 3 sophomores in the committee.
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(b) Find the probability that the committee has at least one representative from each of the senior, junior, and sophomore classes.

fifthist x · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item $$\dfrac{\binom{15}{3}\binom{22}{2}}{\binom{37}{5}}$$

\item $$\dfrac{\binom{37}{5} - \binom{27}{5} - \binom{25}{5} - 
\binom{22}{5} + \binom{15}{5} + \binom{10}{5} + \binom{12}{5}}{\binom{37}{5}}$$
\end{enumerate}

Exercise 1.55

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Exercise 1.55

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