Question

) eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First, the women chose the chairs from amongst the chairs marked 1 to 4, then the men selected the chairs from amongst the remaining, marked 5 to 8. The number of possible arrangements is

Answer 1

Step-by-step explanation:

irst women can take any of the chairs marked 1 to 4 in 4 different way.

Second women 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 women can take seat =4×34×3

⇒4P2⇒4P2

4P2=4!(4−2)!4P2=4!(4−2)!

=4×3×2×12×1=4×3×2×12×1

=12=12

After two women are seated 6 chairs remains

First man take seat in 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 seat in any of the remaining 4 chairs in 4 different ways.

So,total no of ways in which men can take seat =6×5×46×5×4

⇒6P3⇒6P3

6P3=6!(6−3)!6P3=6!(6−3)!

⇒6×5×4×3×2×13×2×1⇒6×5×4×3×2×13×2×1

⇒120⇒120

Hence total number of ways in which men and women can be seated =120×12120×12

⇒1440⇒1440

Hence (B) is the correct answer.