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
$406$
$130$
$142$
$136$
In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than $32$ teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city is
If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
Number of integral solutions to the equation $x+y+z=21$, where $x \geq 1, y \geq 3, z \geq 4$, is equal to $..........$.
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls $?$