Answer:
Solving steps:
Question:5 boys and 4 girls are randomly arranged to sit in a row. find the probability that all girls sit together.
Find:the probability that all girls sit together.
Solution: 5 boys and 4 girls, 9 kids in all, can be seated in a row in 9! ways. In order to find the number of ways, where the 4 girls are seated together, we place them in an imaginary group Z, so that they are not separated in the seating arrangements. Now we have 6 entities, namely 5 boys and one group of girls, and the number of ways of their seating is 6!. For each of these 6! ways, the 4 girls can be seated within the group Z in 4! ways. So the number of ways in which the 4 girls are seated together, is 6!/4!.
So the probability, as requested, is (6!4!)/9! = 24/(7x8x9) = 1/21