Mahesh has $6$ friends. In how many ways can he invite one or more friends for dinner?

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples,is

The number of ways $16$ identical cubes,of which $11$ are blue and the rest are red,can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes,is

The least value of $n$ such that ${ }^{(n-1)} C_3 + { }^{(n-1)} C_4 > { }^n C_3$ is:

The number of non-negative integral solutions of $x_1+x_2+x_3+x_4=10$ is

The total number of ways of selecting six coins out of $20$ one rupee coins,$10$ fifty paise coins,and $7$ twenty-five paise coins is: