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

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Question 1183998: 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?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Assuming those names are 3 girls and 2 boys, the arrangements are either GGGBB or BBGGG; that's 2 possibilities.

Within the group of 2 boys the number of possible arrangements is 2!=2; within the group of 3 girls the number of possible arrangements is 3!=6.

The total number of ways of arranging the 5 people is 2*2*6=24.

The total number of possible arrangements without restrictions is 5!=120.

The probability that the boys will be next to each other and the girls will be next to each other is 24/120 = 1/5.

ANSWER: 1/5

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

A professional problems' composer would formulate the problem as follows:


        "Three girls and two boys 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?"


without stressing the reader to guess which names mean girls and which mean boys.


But the person, who came from puzzles, will formulate exactly as in the original post.