SOLUTION: Valentina, Luke, Sally, Han and Mae are to be placed in a line in random order. What is the probability that the boys will be next to each other and the girls will all

Question 1183995: Valentina, Luke, Sally, Han and Mae are to be placed in a line in random order.

What is the probability that the boys will be next to each other and the girls will all be next to each other?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the possible arrangements, without any restrictions, are 5! = 120.
if the boys need to be together, that can happen in 3! arrangements = 6.
if the girls need to be together, that can happen in 2! arrangements = 2.
that would be a total of 6 * 2 = 12 possible arrangements if all the boys are on the left and another total of 2 * 6 = 12 possible arrangements if all the girls are on the left.
you get 24 possible arrangements out of 120 possible arrangements, giving you a probability of 24/120 = 1/5.

let the boys be 1,2,3.
let the girls be a,b.

when the girls are on the left, you get:

ab123
ab132
ab213
ab231
ab312
ab321
ba123
ba132
ba213
ba231
ba312
ba321

that's a total of 12.

when boys are on the left and the girls are on the right, that's another 12 possible arrangements, for a total of 24 out of 120 = 1/5.

as far as i can tell, the probability is 1/5.

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