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6.Permutation and Combination
easy
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 $b +3\,g$ is equal to.
A
$17$
B
$16$
C
$15$
D
$14$
(JEE MAIN-2022)
Solution
${ }^{b} C_{3} \times{ }^{g} C_{2}=168$
$b(b-1)(b-2)(g)(g-1)=8 \times 7 \times 6 \times 3 \times 2$
$b+3 g=17$
Standard 11
Mathematics