In how many ways can a team of $11$ players be formed out of $25$ players,if $6$ out of them are always to be included and $5$ are always to be excluded?

If $^{n}C_{8} = ^{n}C_{2}$,find $^{n}C_{2}$.

In an election,the number of candidates is $1$ more than the number of persons to be elected. If the voters can cast their votes in $254$ ways,find the number of candidates. ($A$ voter cannot cast more votes than the number of persons to be elected.)

If $1 \times 1! + 2 \times 2! + 3 \times 3! + \ldots + n \times n! = 11! - 1$,then the maximum value of ${}^n C_r$ is

If ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$,then the value of $r$ is

Number of ways of arranging $8$ identical books into $4$ identical shelves where any number of shelves may remain empty is equal to