3 Couples in a Circle --- II
Probability
Level
3
3 married couples go out for dinner and are seated randomly around a circular table for six people. What is the probability that exactly and only 2 of the 3 couples are seated together?
The answer is 0.2.
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1 solution
Fix a couple L(2x) and combine with the other couple say M together (2x). M can only sit in front of L since if they sit next to each other, there will be 3 couples together. The remaining couple can change places (2x).
We can select 2 out of 3 couples in three ways (3x).
The number of ways is 2x2x2x3 = 24.
Number of ways 6 ppl can sit in a circle = 5!
Probability of exactly 2 couples seated together = 24/120 = 0.2