1.

There are seven boys and four girls in a row. In how many ways can they be seated in the row so that all the girls do not sit together ?

Answer»

11! - 8! x 4!



without any restriction, 11 persons can sit in 11! ways, If we take all the GIRLS together as ONE, the total number of persons will be 7 + 1 = 8, who can sit in 8! ways and the FOUR girls can sit in 4! ways among themselves. So, when all the girlssit together the number of ways = 8!x 4!
When they don't sit together, the total number of ways = 11! - 8! x 4!



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