(B) There are $3$ men and $2$ women,totaling $5$ people. Since there are $2$ sides of the bus with $3$ seats each,there are $6$ total seats available.

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(B) There are $3$ men and $2$ women,totaling $5$ people. Since there are $2$ sides of the bus with $3$ seats each,there are $6$ total seats available. First,we choose $5$ seats out of $6$ to seat the $5$ people,which can be done in $^6C_5$ ways. Then,the $5$ people can be arranged in these $5$ chosen seats in $5!$ ways. Therefore,the total number of ways is $^6C_5 \times 5!$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

The number of ways to seat $3$ men and $2$ women in a bus such that the total number of seated men and women on each side is $3$ is:

A
$5!$
B
$^6C_5 \times 5!$
C
$6! \times ^6P_5$
D
$5! + ^6C_5$

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Permutations and Combinations

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

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EasyAP EAMCET 2005

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The number of ways to seat $3$ men and $2$ women in a bus such that the total number of seated men and women on each side is $3$ is:

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