QJEEM22Maa81b: JEE Main 2022 Mathematics - Class 11 JEEM22Maa81b Solution: A class contains b boys and g girls. If the number of ways of…

${}^b{C_3}\,.\,{}^g{C_2} = 168$

$\Rightarrow {{b(b - 1)(b - 2)} \over 6}\,.\,{{g(g - 1)} \over 2} = 168$

$\Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = {2^5}{.3^2}.7$

$\Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = 6\,.\,7\,.\,8\,.\,3\,.\,2$

$\therefore$ $b = 8$ and $g = 3$

$\therefore$ $b + 3g = 17$