If a person has $3$ coins of different denominations,the number of different sums that can be formed is

The number of ways to select one or more books from $6$ books is:

The number of ways of forming the ordered pairs $(p, q)$ such that $p > q$ by choosing $p$ and $q$ from the first $50$ natural numbers is

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

If $4$ red balls and $5$ green balls are selected from $n$ balls,and the sum of both selections is greater than ${}^{n+1}C_4$,then the value of $n$ is equal to:

The number of integral solutions to the equation $x+y+z=21$,where $x \geq 1, y \geq 3, z \geq 4$,is equal to $..........$.