Question

A bag contains 3 red marbles, 2 green, 1 lavender, 2 yellow and 2 orange.How many sets of 5 marbles include at most one of the red ones?

Answer 1

any attempt?

Answer 2

Use hypergeometric distribution where:K=3, k=1, N=20, n=5
\[P(k)=\frac{ \left(\begin{matrix}K \\ k\end{matrix}\right)\left(\begin{matrix}N-K\\ n-k\end{matrix}\right) }{\left(\begin{matrix}N \\ n\end{matrix}\right) }\rightarrow N_{1 red}=\left(\begin{matrix}10\\ 5\end{matrix}\right)P(1)=\left(\begin{matrix}3 \\ 1\end{matrix}\right)\left(\begin{matrix}7 \\ 4\end{matrix}\right)=105\]