The number of ways five alphabets can be chosen from the alphabets of the word $MATHEMATICS$, where the chosen alphabets are not necessarily distinct, is equal to :

If $^{2n}{C_2}{:^n}{C_2} = 9:2$ and $^n{C_r} = 10$, then $r = $

The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is

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

There are three bags $B_1$,$B_2$ and $B_3$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from bag $B_1$ and placed in bag $B_2$, then a ball is drawn from bag $B_2$ and placed in bag $B_3$, then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed, if same colour balls are used in first and second transfers (Assume all balls to be different) is

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:

at most $3$ girls?