(B) Total number of ways to select $2$ boys from $5$ and $3$ girls from $7$ is given by $^5C_2 \times ^7C_3 = 10 \times 35 = 350$.If both girls $A$ an

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(B) Total number of ways to select $2$ boys from $5$ and $3$ girls from $7$ is given by $^5C_2 \times ^7C_3 = 10 \times 35 = 350$.If both girls $A$ and $B$ are in the same team,we need to select $2$ boys from $5$ and $1$ more girl from the remaining $5$ girls (since $A$ and $B$ are already selected). The number of such ways is $^5C_2 \times ^5C_1 = 10 \times 5 = 50$.The number of teams where $A$ and $B$ are not together is the total number of teams minus the teams where both are present.Required number of ways $= 350 - 50 = 300$.

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

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

MHT CET 2024 All MHT CET

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

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Permutation and Combination

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Definition of combinations, Condition combinations

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

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