There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
Choose the correct choice from the following options.
A) 1/12!  B) 6!5!/12!  C) 6!6!/12!  D) 2∗6!6!/12!  E) 6!7!/12!
If girls are alternate, then only no 2 girls can be together.   So among 12 places, girls can be seated in 6 alternate places in 6! ways.   And boys can be seated in the remaining 6 places in 6! ways.   Therefore total number of ways = 6! * 6!   But there could be 2 such arrangements--&gt;   1. When first place is filled by a girl   2. When first place is filled by a boy   Therefore total number of ways = 2*6! * 6!   Also total number of ways to fill 12 places = 12!   Hence probability =2∗6!6!/12!   Answer:2∗6!6!/12!
<result>D</result>
There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two girls sit together?