In how many different ways can 7 boys and 3 girls sit in a row such that all the three girls do not sit together ?

• A. 3186880
• B. 3086880
• C. 3386880
• D. 3286880

Answer: (C)

A total of (7 + 3) persons = 10 personal can sit in 10! ways.If we consider three girls as one unit, total persons = 7 + = 8 (here all three girls sit together).No. of ways = 81 and the three girls can be arranged in 31 ways among themselves.So, the total number of ways when three girls sit together = 81 x 31When the girls don't sit together, number of ways = 101 - (81 x 31) = 81 (10 x 9 - 6) = 81 x 84 = 3386880