If ${}^n C_7 = {}^n C_6$,then ${}^n C_2 = $

The product of any $r$ consecutive natural numbers is always divisible by

In an election,the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

If $^8C_r = ^8C_{r+2}$,then the value of $^rC_2$ is

There are $10$ persons named $A, B, \dots, J$. We have space to keep only $5$ of them. If $A$ must be included,and $G$ and $H$ must not be included in the group of $5$,in how many ways can we arrange the group in a row?