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The answer to this question uses the phrase "multinomial of size".

What is the definition of the size of a multinomial? They are using a negative multinomial.

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The size is a metric on on an elementary event, which is defined as a sequence of multinomial events before a stopping event occurs. Each multinomial event can have $n$ outcomes where $n \geq 2$. It is not a metric on the number of outcomes of each trial.

DavidW
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