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 ?

• A. 10! - 7! x 3!
• B. 11! - 8! x 3!
• C. 11! - 8! x 4!
• D. 11! - 7! x 4!

Answer: (C)

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 girls  sit together the number of ways = 8!  x 4!When they don't sit together, the total number of ways = 11! - 8! x 4!