The number of natural numbers,between $212$ and $999$,such that the sum of their digits is $15$,is . . . . . .

The number of $3$-$digit$ odd numbers,whose sum of digits is a multiple of $7$,is

$A$ box contains $5$ blue, $6$ yellow, and $4$ red balls. The number of ways of drawing $8$ balls containing at least two balls of each color is:

The number of ways in which a committee of $7$ members can be formed from $6$ teachers,$5$ fathers,and $4$ students in such a way that at least one from each group is included and teachers form the majority among them,is

Three schools send $2, 4,$ and $6$ students,respectively,to a summer camp. The $12$ students must be accommodated in $6$ rooms numbered $1, 2, 3, 4, 5, 6$ in such a way that each room has exactly $2$ students and both are from the same school. The number of ways the students can be accommodated in the rooms is

If $\frac{{}^{n + 2}C_6}{{}^{n - 2}P_2} = 11$,then $n$ satisfies the equation