A class contains b boys and g girls. If the n | vedclass

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(A) The number of ways to select $3$ boys from $b$ boys and $2$ girls from $g$ girls is given by ${}^{b}C_{3} 	imes {}^{g}C_{2} = 168$.Expanding the

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$17$

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(A) The number of ways to select $3$ boys from $b$ boys and $2$ girls from $g$ girls is given by ${}^{b}C_{3} 	imes {}^{g}C_{2} = 168$.Expanding the combinations: $\frac{b(b-1)(b-2)}{3 	imes 2 	imes 1} 	imes \frac{g(g-1)}{2 	imes 1} = 168$.$b(b-1)(b-2) 	imes g(g-1) = 168 	imes 12 = 2016$.Testing integer values for $b$ and $g$: If $b=8$,then ${}^{8}C_{3} = \frac{8 	imes 7 	imes 6}{6} = 56$.Then ${}^{g}C_{2} = \frac{168}{56} = 3$.For ${}^{g}C_{2} = 3$,we have $\frac{g(g-1)}{2} = 3$,so $g(g-1) = 6$,which gives $g=3$.Thus,$b=8$ and $g=3$.Calculating $b + 3g = 8 + 3(3) = 8 + 9 = 17$.

$A$ 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.

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