(D) Let the group of $n$ boys be $B$ and the group of $n$ girls be $G$. Since all boys must be together and all girls must be together,we treat the gr

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(D) Let the group of $n$ boys be $B$ and the group of $n$ girls be $G$. Since all boys must be together and all girls must be together,we treat the group of boys as one unit and the group of girls as one unit. There are $2!$ ways to arrange these two units (either $BG$ or $GB$). Within the group of boys,the $n$ boys can be arranged in $n!$ ways. Within the group of girls,the $n$ girls can be arranged in $n!$ ways. Thus,the total number of ways is $2! \times n! \times n! = 2(n!)^2$. Comparing this with the given options,none of the options $A, B,$ or $C$ match this value.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the boys are together and all the girls are also together is equal to

TS EAMCET 2023 All TS EAMCET

A
the number of ways in which $n$ boys and $n$ girls can be arranged in a row
B
the number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the girls are together
C
the number of ways in which $n$ boys and $n$ girls can be arranged in a row such that no two girls are together
D
none of these

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the boys are together and all the girls are also together is equal to

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