Number of ways selecting a captain from 15 players = $ \begin{pmatrix} 15 \\ 1 \end{pmatrix}$
Number of ways selecting remaining team members from remaining 14 players
= $ \begin{pmatrix} 14 \\ 10 \end{pmatrix}$
The number of different ways to choose a team of 11 from a pool of 15 players and also select a captain
=$ \begin{pmatrix} 15\\ 1 \end{pmatrix}$ *$ \begin{pmatrix} 14 \\ 10 \end{pmatrix}$=15*13*11*7= 11 *$ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$
Alternate Method:
Number of ways of selecting 11 players from 15 players = $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$
Number of ways of selecting a captain from selected 11 players=11
The number of different ways to choose a team of 11 from a pool of 15 players and also select a captain=$11 *\begin{pmatrix} 15 \\ 11 \end{pmatrix}$
Hence,Option(B)11 *$ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ is The correct choice.
