Question 313342: There are 4 boys and 3 girls. What is the probability the boys and girls sit alternately?
Ans 1/35 Answer by Theo(13342) (Show Source):
The probability that the first slot will be taken by a boy is 4/7
the probability that the second slot will be taken by a girl is 3/6
The probability that the third slot will be taken by a boy is 3/5
Then 2/4
Then 2/3
Then 1/2
Then 1/1
the probability that all of this will occur is 4/7 * 3/6 * 3/5 * 2/4 * 2/3 * 1/2 * 1/1 which comes out to be (4*3*3*2*2*1*1)/(7*6*5*4*3*2*1) which comes out to be 1/35.
Since this arrangement can only happen in one way, then that's your answer.
