Probability: # of Permutations from r Choices of n Objects

[Michael Si]

There are n objects, within which there are p identical objects. Now, suppose if you randomly choose r objects from the n objects. How many permutations will you get from the r objects you choose?

 

[cellotim]

So we have n balls, p are identical. Are the rest not identical? I.e. are exactly p identical or at least p identical?

Suppose it's exactly p. One way is to do it by cases. Choose k from the n-p distinct objects and r-k from the p identical. In that case you have a sum over k=0...r.

Now imagine r identical balls, choose r-k to remain identical. Now paint the remaining k with distinct numbers from 1 to n-p. How many possibilities?

 

[HallsofIvy]

There are n objects, within which there are p identical objects. Now, suppose if you randomly choose r objects from the n objects. How many permutations will you get from the r objects you choose?

Your question is ambiguous. Are there n containers each with p objects? And the objects are identical only within each container- different containers contain different objects? Or are there a total of p (or np?) identical objects?