Question

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 ______.

Answer 1

Given, b boys and g girls

Also given total ways of selecting 3 boys and 2 girls which will be \(\begin{array}{l}^bC_3\cdot ^gC_2 = 168\end{array}\)

So, \(\begin{array}{l} \Rightarrow \frac{b\left(b-1\right)\left(b-2\right)}{6}\cdot\frac{g\left(g-1\right)}{2}=168 \end{array}\)

\(\begin{array}{l}\Rightarrow b\left(b – 1\right) \left(b – 2\right) g\left(g – 1\right) = 2^5\cdot 3^2\cdot 7\\ \Rightarrow b\left(b – 1\right) \left(b – 2\right) g\left(g – 1\right) = 6. 7. 8. 3. 2\end{array}\)

∴ b = 8 and g = 3

∴ b + 3g = 17