Question

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

• A. $1550$
• B. $1440$
• C. $1444$
• D. $1500$

Answer 1

The correct option is B $1440$

First woman can take any of the chair marked $1$ to $4$ in $4$ different ways. Second woman can take any of the remaining $3$ chairs from those marked $1$ to $4$ in $3$ different ways.

So, total no. of ways in which woman can take seat$=4\times 3{⟹}^4{P}_2⟹12$

After $2$ women are seated $6$ chairs, first man can take any of the $6$ chairs in $6$ different ways.

Second man can take seat in any of the remaining $5$ chairs in $5$ different ways.

Third man can take any of the remaining$4$ chairs, in $4$ different ways.

$\therefore \text{Total no. of ways}=6\times 5\times 4{=}^6{P}_3=120$

$\text{Total no. of ways in which men and women can be seated}=120\times 12=1440$