If $^{20}{C_{n + 2}}{ = ^n}{C_{16}}$, then the value of $n$ is

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is

If $^n{C_{12}} = {\,^n}{C_6}$, then $^n{C_2} = $

There are $15$ persons in a party and each person shake hand with another, then total number of hand shakes is

The number of ways to give away $25$ apples to $4$ boys, each boy receiving at least $4$ apples, are