There are two ways to express the negative binomial probability function where the "combination" can be expressed differently.

(r + x - 1 choose x) is equivalent to (r + x - 1 choose r -1)

I know I can just accept that there are two ways to express the function but I am trying understand how they are the same.

Does this mean that x = r -1?

(r + x - 1 choose x) is equivalent to (r + x - 1 choose r -1)

I know I can just accept that there are two ways to express the function but I am trying understand how they are the same.

Does this mean that x = r -1?

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