JEE MAIN - Mathematics (2022 - 28th July Evening Shift - No. 16)
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
17
Explanation
$${}^b{C_3}\,.\,{}^g{C_2} = 168$$
$$ \Rightarrow {{b(b - 1)(b - 2)} \over 6}\,.\,{{g(g - 1)} \over 2} = 168$$
$$ \Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = {2^5}{.3^2}.7$$
$$ \Rightarrow b(b - 1)(b - 2)\,\,\,\,\,\,g(g - 1) = 6\,.\,7\,.\,8\,.\,3\,.\,2$$
$$\therefore$$ $$b = 8$$ and $$g = 3$$
$$\therefore$$ $$b + 3g = 17$$
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