In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

If $^{15}C_{3r} = ^{15}C_{r+3}$,find the value of $r$.

$A$ class contains $b$ boys and $g$ girls. If the number of ways of selecting $3$ boys and $2$ girls from the class is $168$,then $b + 3g$ is equal to.

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

An engineer is required to visit a factory for exactly $4$ days during the first $15$ days of every month,and it is mandatory that no two visits take place on consecutive days. The number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is: