In order to select a debating team to represent a school, $7$ students from class XII and $13$ students from class XI were shortlisted and were undergoing trials. The coach had to select a team of $5$ students, out of which at least two students should be from each class. One out of the $5$ students was to be named as team leader, who was to be from class XII. Two teams with the same members but different leaders are considered to be two different teams. The number of different teams the coach can select is
- $2 \times\left(\left(\begin{array}{l}7 \\ 2\end{array}\right) \times\left(\begin{array}{c}13 \\ 3\end{array}\right)+\left(\begin{array}{l}7 \\ 3\end{array}\right) \times\left(\begin{array}{c}13 \\ 2\end{array}\right)\right)$
- $\left(\begin{array}{l}7 \\ 2\end{array}\right) \times\left(\begin{array}{c}13 \\ 3\end{array}\right)+\left(\begin{array}{l}7 \\ 3\end{array}\right) \times\left(\begin{array}{c}13 \\ 2\end{array}\right)$
- $2 \times\left(\begin{array}{l}7 \\ 2\end{array}\right) \times\left(\begin{array}{c}13 \\ 3\end{array}\right)+3 \times\left(\begin{array}{l}7 \\ 3\end{array}\right) \times\left(\begin{array}{c}13 \\ 2\end{array}\right)$
- $3 \times\left(\begin{array}{l}7 \\ 2\end{array}\right) \times\left(\begin{array}{c}13 \\ 3\end{array}\right)+2 \times\left(\begin{array}{l}7 \\ 3\end{array}\right) \times\left(\begin{array}{c}13 \\ 2\end{array}\right)$
