Question

in how many ways can 5girls and 3 boys be seated in a row with 11 chairs so that no two boys are together?

Answer 1

Reqd. no. of ways=5P5×6P3
=14400

Answer 2

FIVE GIRLS CAN be placed in 5! ways

set the positions for girls first -g-g-g-g-g-

now see the dash . at the dashes boys can be placed fulfilling the requirement of the question.

so there are 3 boys and 6 places for boys to occupy.

it can be done in 6*5*4 ways= 120.

so total no of ways= 5! * 120 = 120*120 = 14400 ways