Would you be able to solve the problem if the balls were distinguishable from one another?
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.
Would you be able to solve the problem if the balls were distinguishable from one another?
I don't have emotions and sometimes that makes me very sad.
Unfortunately, No.
All r balls are indistinguishable. it would be easy for distinguishable.
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
Which part are you having difficulty with? Calculating the size of the numerator or the denominator (or both)?
I don't have emotions and sometimes that makes me very sad.
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