(C) Total number of ways to select $2$ girls from $5$ and $3$ boys from $7$ without any restriction is given by $^5C_2 \times ^7C_3 = 10 \times 35 = 3

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(C) Total number of ways to select $2$ girls from $5$ and $3$ boys from $7$ without any restriction is given by $^5C_2 \times ^7C_3 = 10 \times 35 = 350$.If both specific boys $A$ and $B$ are in the team,we need to select $1$ more boy from the remaining $5$ boys and $2$ girls from $5$ girls. The number of such teams is $^5C_1 \times ^5C_2 = 5 \times 10 = 50$.Therefore,the number of teams where $A$ and $B$ are not together is $350 - 50 = 300$.

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

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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 members of the same team,is

JEE MAIN 2019 All JEE MAIN

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

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Definition of combinations, Condition combinations

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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 members of the same team,is

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