Number of integral solutions to the equation $x+y+z=21$, where $x \geq 1, y \geq 3, z \geq 4$, is equal to $..........$.
Number of integral solutions to the equation $x+y+z=21$, where $x \geq 1, y \geq 3, z \geq 4$, is equal to $..........$.
- [JEE MAIN 2023]
- A
$104$
- B
$105$
- C
$103$
- D
$102$
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The students $S _{1}, S _{2}, \ldots \ldots, S _{10}$ are to be divided into $3$ groups $A , B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is ........ .
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- [JEE MAIN 2021]