If $(n+2)! = 2550(n!)$,find $n$.

On the occasion of the Deepawali festival,each student of a class sends greeting cards to all the others. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

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

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $1$ particular player is to be excluded?

Ten persons,among whom are $A, B$,and $C$,are to speak at a function. The number of ways in which they can speak if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is: