A PERMUTATION PROBLEM! HELP D:?

Question

Petey is on the same round table as his brother, John and his sister, Jane. If they sit next to each other they will start fighting. If the seats for the table as chosen at random, find the probability that exacly 2 of the siblings are sitting together.

There are 12 seats at the circular table.

Answer 1

Favorite Answer

treating clockwise & anticlockwise as different

seat 2 siblings from 3 anywhere : 3P2 = 6 ways,

and treat them as the reference

the 3rd sibling can be seated in any of (10-2 adjoining) = 8 ways

the remaining 9 can be seated in 9P9 = 9! ways

stipulated seating arrangements = 6*8*9!

total seating arrangements = (12-1)!

probability = 6*8*9!/11!

= 6*8/(10*11)

= 24/55

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