Find the number of ways of selecting $4$ pens and $3$ pencils from a packet of $8$ pens and $5$ pencils.

From all the English alphabets,five letters are chosen and are arranged in alphabetical order. The total number of ways,in which the middle letter is $M$,is:

There are $6$ different novels and $3$ different poetry books on a table. If $4$ novels and $1$ poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle,then the number of such possible arrangements is

The number of ways a committee of $8$ members can be formed from a group of $10$ men and $8$ women such that the committee contains at most $5$ men and at least $5$ women is:

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

If the total number of $m$-element subsets of the set $A = \{a_{1}, a_{2}, \ldots, a_{n}\}$ is $k$ times the number of $m$-element subsets containing $a_{4}$, then $n$ is