Help with understanding Bose-Einstein value

[isacmlee]

I can't seem to understand the explanation to this question: "How many ways are there to choose k times from a set of n objects with replacement?"

The explanation is in the image below. I don't understand why it is (n + k -1) choose k. How does he get to (n + k - 1)? I understand what he's saying about n - 1 |'s and k *'s. I would appreciate any advice on understanding this. Thank you!

 

[fed2]

usually when you see that formula the best explanation is the 'divider rule' https://web.stanford.edu/class/archive/cs/cs109/cs109.1166/pdfs/05 Combinatorics.pdf

i always think of it as number of unique histograms.

i didn't read the whole thinger madoodle you posted, just saw the formula and recognized maximum liklihood answer.

 

[isacmlee]

usually when you see that formula the best explanation is the 'divider rule' https://web.stanford.edu/class/archive/cs/cs109/cs109.1166/pdfs/05 Combinatorics.pdf

i always think of it as number of unique histograms.

i didn't read the whole thinger madoodle you posted, just saw the formula and recognized maximum liklihood answer.

Thank you!!! That was so much easier to understand than the way the author approached it.

 

[fed2]

its sort of weird to me they named it the 'bose-einstein value'. The argument was stolen from combinatorics time in memorial, probably bernoulli or newton i think is associated with negative binomials?