(C) We have $3$ men and $3$ women to be arranged in $6$ seats.The first and last seats must be occupied by men.Step $1$: Select $2$ men out of $3$ for

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(C) We have $3$ men and $3$ women to be arranged in $6$ seats.The first and last seats must be occupied by men.Step $1$: Select $2$ men out of $3$ for the first and last seats and arrange them in $P(3, 2) = 3 \times 2 = 6$ ways.Step $2$: The remaining $4$ people ($1$ man and $3$ women) can be arranged in the remaining $4$ middle seats in $4! = 24$ ways.Total number of arrangements $= 6 \times 24 = 144$.

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

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The number of ways in which $3$ men and $3$ women can be arranged in a row of $6$ seats,such that the first and last seats must be filled by men is

AP EAMCET 2024 All AP EAMCET

A
$720$
B
$36$
C
$144$
D
$72$

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Class 11

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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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The number of ways in which $3$ men and $3$ women can be arranged in a row of $6$ seats,such that the first and last seats must be filled by men is

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