(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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Class 11

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Chapter

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

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

The number of ways in which ten candidates $A_1, A_2, \dots, A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is:

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