A class contains b boys and g girls. If the number of ways of...

Given, $b\text{boys and g girls}$

Also given total ways of selecting $3\text{boys and 2 girls}$ which will be $C3 b \times C2 g = 168$

$⇒ \dfrac{b\left(b - 1\right)\left(b - 2\right)}{6} \times \dfrac{g\left(g - 1\right)}{2} = 168$

$⇒ b\left(b - 1\right)\left(b - 2\right)g\left(g - 1\right) = 7 \times 6 \times 4 \times 3 \times 2 \times 2$

$⇒ b\left(b - 1\right)\left(b - 2\right)g\left(g - 1\right) = 8 \times 7 \times 6 \times 3 \times 2$

Now on comparing both side we get, $b = 8$ and $g = 3 ⇒ b + 3g = 8 + 9 = 17$