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?
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?
$4$ men and $4$ women are to be seated in a row such that the women occupy the even places.
The $5$ men can be seated in $5 !$ Ways. For each arrangement, the $4$ women can be seated only at the cross marked places (so that women occupy the even places).
Therefore, then women can be seated in $4!$ ways.
Thus, possible number of arrangements $=4 \times 5 !=24 \times 120=2880$
Similar Questions
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
- [JEE MAIN 2024]
If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
The total number of three-digit numbers, with one digit repeated exactly two times, is
The total number of three-digit numbers, with one digit repeated exactly two times, is
- [JEE MAIN 2022]
The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-
The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-