For P(N=k) = k-1Cr-1 × pr × (1-p)k-r, we have a term and definition in Statistics.

Consider a sequence of independent trials with the same probability p of success in each trial. The number of trials up to and including the rth success has the negative Binomial distribution with parameters n and r. If the random variable N has the negative binomial distribution with parameters n and r, then
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