From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

Out of $6$ books,in how many ways can a set of one or more books be chosen?

If $5$ dice are rolled simultaneously,then the number of ways of getting a total of $7$ on their faces is:

There are $25$ candidates for $12$ positions,out of which $5$ are from the reserved category. If $3$ positions are reserved and the remaining are open,in how many ways can the selection be made?

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

The least value of a natural number $n$ such that $\binom{n-1}{5} + \binom{n-1}{6} < \binom{n}{7}$ is: