My Math Forum Randomly selecting N from N

 February 23rd, 2012, 11:19 AM #1 Newbie   Joined: Feb 2012 Posts: 1 Thanks: 0 Randomly selecting N from N Dear all, I am a newcomer here, but am looking for some advice. I believe this problem must be well known, but I am not sure where to look. This is a simpler version of the real problem, but I am hoping that if I can get a look at how this was solved it will help me with my real problem. Imagine I have N equally likely choices (boxes) (I initially thought about 100, but liked the idea of generalising it), and make N independent choices, what is the most likely number of independent boxes I will fill? Once a box has been chosen it can clearly be chosen again, or else it becomes rather a boring problem. Is there anything which I can do to think about the distribution of independent boxes filled around this most likely number? So, does anyone have any idea where I should be looking for an approach to this? Many thanks for any help you can offer. Mike
 February 23rd, 2012, 05:30 PM #2 Newbie   Joined: Feb 2012 Posts: 5 Thanks: 0 Re: Randomly selecting N from N A well known version of this question concerns the probability of two students, in a class of a given size, having the same birthday.

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