Question

The number of ways so that $3$ men and $2$ women can sit in a bus such that the total number of sitting men and women on each side is $3$?

• A. $5!$
• B. ${}^6{C}_5\times 5!$
• C. $6!\times {}^6{P}_5$
• D. $5!\times {}^6{C}_5$

Answer 1

The correct option is B

${}^6{C}_5\times 5!$

Explanation for the correct option(s)

Find the the total number of ways

Consider the given data

$3$ men and $2$ women equals to $5$

$5$ people will sit in the bus that can be expressed in $5!$ ways

$6$ seats can be filled by $5$ people in the bus in ${}^{6}C_5$ ways

Hence, the total number of ways are equal to ${}^6{C}_5\times 5!$

Therefore, the correct answer is Option B.