Question

The number of ways in which a team of $11$ players be formed out of $25$ players, if $6$ out of them are always to be included and $5$ always to be excluded is

Answer 1

Since $5$ players are always to be excluded and $6$ players always to be included, therefore $5$ players are to be chosen from $14$.

Hence required number of ways is ${}^{14}{C}_5=2002$.