SOLUTION: A group consisting of 3 boys and 2 girls is to line-up in a row for a photograph. In how many ways may this be done assuming that (a) there are no restrictions? (b) the boys and

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Question 396177: A group consisting of 3 boys and 2 girls is to line-up in a row for a photograph. In how many
ways may this be done assuming that
(a) there are no restrictions?
(b) the boys and the girls are each to stand together?
(c) only the two girls are to stand together?
(d) Rachel and Jonathan must not stand together?
Answer by sudhanshu_kmr(1152) (Show Source):
You can put this solution on YOUR website!
a)
no. of ways to arrange 5 persons if no restrictions = 5! = 120

b)
no. of ways to arrange 3 boys together = 3! = 6
no. of ways to arrange 2 girls together= 2! = 2

no. of ways to arrange boys and girls together in a row = 6 * 2 * 2 = 24
( as group of boys and group of girls can also arrange by 2 ways )

C)
no. of ways when 2 girls are together = 4! * 2! = 48
(assume 2 girls as a single person, then total 4 persons)

d)
no. of ways when Rachel and Jonathan are together = 4! * 2! = 48

no. of ways when both are not together = total no. of ways - 48
= 120 - 48
= 72

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