Question

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is

• A. $200$
• B. $300$
• C. $500$
• D. $350$

Answer 1

Answer: (B)

$300$

Given :Girls-$5$ and boys-$7$

Team members:Girls-$2$ and boys-$3$

Total number of ways${=}^5{C}_2{\cdot }^7{C}_3$

consider when $A$ and $B$ are always included${=}^5{C}_1{}^5{C}_2$ as only $1$ boy and $2$ girls are to be selected

Require number of ways
$=$ Total number of ways $-$ When $A$ and $B$ are always included.
${=}^5{C}_2{\cdot }^7{C}_3{-}^5{C}_1{}^5{C}_2=300$.