There are 'n' homes on the circumference of a circle.In each home there reside husband and wife.People of each home know only their neighbors (on both sides) and no one else.once,all the people of ten homes meet at a party.men dance with women.what is the probability that people do not know whom they danced with?
try out for n=5.
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3 comments:
seems to be a difficult problem.i and suhas spent 5 hrs togather to arrive at the solution to general 'n'.
Each man knows three women (own wife, 2 neighbors' wives) and vice-versa. So for n>3, probability that a man does not know who he danced with, = (n-3)/n. For n<=3, probability = 0.
Dear anonymous,
At the first instance your solution is not correct.Because the questions aks foe the probability that " all the dancers donot know each other ".You have answered to one person which is not complete.
Then, your idea is basically wrong.Calculating individual probabilities and then multiplying is not possible because the probabilities are not independent.If man 1 pairs wom 2 , then man 2 has only two options left.this is only an example,for the situation is much more complicated as choice of one person depends on other(s).
Try out the solution. If you identify yourself by sending a mail to my g mail ( which you will find in my profile ), I shall write the solution in detail.
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