Exams Joint Entrance Examination Mathematics Permutations and Combinations Question 137 Question 137 of 278 Medium NUMERICAL
A class contains b b b boys and g g g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g b+3g b + 3 g is equal to \_\_\_\_\_\_\_\_.
Answer: 17
Solutions · 1 Post your solution Official solution
\[\binom{b}{3}\binom{g}{2} = 168 \implies \frac{b(b-1)(b-2)}{6}\cdot\frac{g(g-1)}{2} = 168\]
\[b(b-1)(b-2)\cdot g(g-1) = 2016 = 8\times7\times6\times3\times2\]
Matching factors: b ( b − 1 ) ( b − 2 ) = 8 × 7 × 6 ⇒ b = 8 b(b-1)(b-2) = 8\times7\times6 \Rightarrow b=8 b ( b − 1 ) ( b − 2 ) = 8 × 7 × 6 ⇒ b = 8 ; g ( g − 1 ) = 3 × 2 ⇒ g = 3 g(g-1)=3\times2 \Rightarrow g=3 g ( g − 1 ) = 3 × 2 ⇒ g = 3 .
b + 3 g = 8 + 9 = 17 b+3g = 8+9 = 17 b + 3 g = 8 + 9 = 17 Answer the question to unlock