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 $\mathrm{b}+3 \mathrm{~g}$ is equal to ____________.
Answer (integer)
17
Solution
<p>${}^b{C_3}\,.\,{}^g{C_2} = 168$</p>
<p>$\Rightarrow {{b(b - 1)(b - 2)} \over 6}\,.\,{{g(g - 1)} \over 2} = 168$</p>
<p>$\Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = {2^5}{.3^2}.7$</p>
<p>$\Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = 6\,.\,7\,.\,8\,.\,3\,.\,2$</p>
<p>$\therefore$ $b = 8$ and $g = 3$</p>
<p>$\therefore$ $b + 3g = 17$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Applications
This question is part of PrepWiser's free JEE Main question bank. 135 more solved questions on Permutations and Combinations are available — start with the harder ones if your accuracy is >70%.