1. ## Occupany problem

This is a homework problem that deals with occupancy.

Q: consider r indistinguishable balls and n cells where n > r. The r balls are placed at random into n cells (multiple occupancy is possible). What is the probability P that r balls appear in r preselected cells (one to a cell)?

As we have n > r, there are many empty spaces.

2. ## Re: Occupany problem

Would you be able to solve the problem if the balls were distinguishable from one another?

3. ## Re: Occupany problem

Unfortunately, No.
All r balls are indistinguishable. it would be easy for distinguishable.

4. ## Re: Occupany problem

I usually approach a problem like this by starting with a trivial case, say 2 balls and three cells. What are the possible outcomes?

*** *** *** OXX XOX XXO
OOX OXO XOO OXX XOX XXO

5. ## Re: Occupany problem

Originally Posted by asterisk
I usually approach a problem like this by starting with a trivial case, say 2 balls and three cells. What are the possible outcomes?

*** *** *** OXX XOX XXO
OOX OXO XOO OXX XOX XXO

This would only work if a cell would take only one ball.
but our case here, it is possible to have multiple balls in one cell.

6. ## Re: Occupany problem

Which part are you having difficulty with? Calculating the size of the numerator or the denominator (or both)?

7. ## Re: Occupany problem

Originally Posted by Dason
Which part are you having difficulty with? Calculating the size of the numerator or the denominator (or both)?
the numerator

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