Question

In a playground, 3 sisters and 8 other girls are playing together. In a particular game, how many ways can all the girls be seated in a circular order so that the three sisters are not seated together?

(a) 457993

(b) 3386880

(c) 6544873

(d) 56549

The question was asked in an online quiz.

Asked question is from Counting in section Counting of Discrete Mathematics

Answer 1

Right option is (b) 3386880

For explanation: There are 3 sisters and 8 other girls in total of 11 girls. The number of ways to arrange these 11 girls in a circular manner = (11– 1)! = 10!. These three sisters can now rearrange themselves in 3! ways. By the multiplication theorem, the number of ways so that 3 sisters always come together in the arrangement = 8! × 3!. Hence, the required number of ways in which the arrangement can take place if none of the 3 sisters is seated together: 10! – (8! × 3!) = 3628800 – (40320 * 6) = 3628800 – 241920 = 3386880.