Question

a coach needs 12 players to ride on a float. he randomly selects names. he has 4 freshmen, 13 sophomores, 14 juniors and 8 seniors. what is the probability that the first two names selected are juniors?

Answer 1

The probability that the first two names are juniors is
\[\frac{\left(\begin{matrix}14 \\ 2\end{matrix}\right)\left(\begin{matrix}15 \\ 0\end{matrix}\right)}{\left(\begin{matrix}39 \\ 2\end{matrix}\right)}\]
\[=\frac{7}{3\times 19}\]

Answer 2

or you can do the following
\[\frac{14}{39}\times \frac{13}{38}\]