# Probability of choosing a partner

My problem is: There are 10 boy and 10 girl and we choose couples(boy-girl) randomly. We know 3 guys (Aladar,Bela,Csaba) and 3 girls (Aranka,Bori,Cecilia). What is the probability that Aladar is not in a pair with Aranka, Bori nor Cecilia and Bela in not in a pair with Bori and Cecilia and Csaba is not in a pair with Cecilia. So it is restricted to make pairs where any of the listed couples dance together.

I think maybe I should calculate the probability that 'a' choose 'a' or 'b' or 'c', it's 3/10. And I should add the probability that 'b' choose 'b' or 'c' and 'c' choose 'c', these are 2/10 and 1/10. If I add them together I get 6/10. There I would subtract the probability of the cases I counted multiple times. These are P(a->b|b->b), P(a->c|b->c), P(a->c|c->c), P(b->c|c->c) and all these probabilities are 1/100 so I subtract all of them from 60/100 to get 56/100. This is the opposite of the probability I search for so the solution is 44/100. That's my idea, but it can be wrong.

Andrew

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What are your own thoughts on this? – Henning Makholm Dec 20 '13 at 20:03
I've just got an idea, but I don't know if it is a right one. – Andrew Dec 20 '13 at 21:07
Sorry, Daniel McLaury - it was an accident:( – Andrew Dec 20 '13 at 22:31