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
$406$
$130$
$142$
$136$
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
Team $'A'$ consists of $7$ boys and $n$ girls and Team $'B'$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to
A company has $10$ employes. The company has decided to form a team including atleast three employes and also excluding atleast three employes. Then the number of ways of forming the team is
Number of integral solutions to the equation $x+y+z=21$, where $x \geq 1, y \geq 3, z \geq 4$, is equal to $..........$.
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :