The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line.

$A$ student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select at least one book is $63$,then the value of $n$ 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:

The number of ways in which $6$ distinct rings can be worn on the $4$ fingers of one hand is:

Find the number of ways of selecting $9$ balls from $6$ red balls,$5$ white balls,and $5$ blue balls,if each selection consists of $3$ balls of each colour.

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is: