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rabit and cage, dirichlet principle

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by tanviet » Wed Jun 09, 2010 8:05 pm
I know that gmat have a question in which we have to keep rabits in the cages and number of cages is less than number of rabits. we have to find most unlucky situation. this relate to Dirichlet principle

anyone has this kind of question, pls,post and say about the Dirichlet principle. Pls, say about the princeple just to do this gmat problem. We do not need to study foo far
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by albatross86 » Wed Jun 09, 2010 10:04 pm
I think you are confusing Dirichlet's principle with the Pigeonhole Principle.

This is the case of placing n objects in m boxes.

If the objects and boxes are distinct, and you can put any number of objects in a given box ( 0 to n), then the number of ways is simply m^n (Each box can has n ways of objects being placed in it). This is a special case of a permutation, with repetition allowed.

For indistinguishable objects and boxes, it is a special case of a combination with repetition allowed. Here it would be (m+n-1)! / [ n! (m-1)! ]

Here's an example:


7 accidents occured during the course of the last 7 days. What is the probability that all the accidents happened on the same day?

Can you solve this now?
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