If $^8C_r = ^8C_{r+2}$,then the value of $^rC_2$ is

$^nC_{r+1} + ^nC_{r-1} + 2^nC_r = \dots$

If $(2 \leq r \leq n)$, then ${}^{n}C_{r} + 2 \cdot {}^{n}C_{r+1} + {}^{n}C_{r+2}$ is equal to:

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

There are $7$ identical white balls and $3$ identical black balls. The number of distinguishable arrangements in a row of all the balls,so that no two black balls are adjacent is

$A$ 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.