(A) There are $9$ total seats in a row ($5$ for men and $4$ for women).The even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$ positions,which

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(A) There are $9$ total seats in a row ($5$ for men and $4$ for women).The even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$ positions,which are $4$ in total.The $4$ women can be arranged in these $4$ even places in $4!$ ways.The $5$ men can be arranged in the remaining $5$ odd places $(1^{st}, 3^{rd}, 5^{th}, 7^{th}, 9^{th})$ in $5!$ ways.Total number of arrangements $= 4! \times 5! = 24 \times 120 = 2880$.

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

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It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

A
$2880$
B
$1440$
C
$720$
D
$5760$

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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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It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

Similar Questions

$A$ coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

The number of integers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) such that the number is a multiple of $3$ is:

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