sandy wrote:

Six people are asked to sit down in a circle consisting of eight chairs.Assume that the six people are in fact three couples.What is the probability that at least one of the three wives will sit next to her husband if everybody takes a seat randomly.

P = 6/7

Number of arrangements where at least one wife sits next to her husband:

Using complement rule

That is, P(Event A happening) = 1 - P(Event A not happening)

So, here we get: P(at least 1 matching couple) = 1 - P(zero matching couple)

P(zero matching couple) =6/8 x 4/7 x 2/6

= 1/7

So, P(at least 1 couple) = 1 - P(no couple)

= 1 - 1/7

= 6/7