Question

$5$ men and $4$ women have to be seated in a row such that women occupy even places. In how many ways can the arrangement be done?

• A. $2880$
• B. $30240$
• C. ${}^{10}{C}_5\times 5!$
• D. ${}^5{C}_4\times 10!$

Answer 1

Answer: (A)

$2880$

$\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$

Even place are occupied by men

$5$ Men , $4$ Women

There are $4$ men and $4$ places

Number of arrangements $=4!=24$

Left over places $=5$

Number of women $=5$

Number of rearrangements $=5!=120$

Total number of arrangemets of men and women together

$\Rightarrow 120\times 24$

$\Rightarrow 2880$ Ways

Hence the correct answer is $2880$ Ways