What is the probability of getting a duplicate of a digit in a randomly generated sequence of four digits?(adsbygoogle = window.adsbygoogle || []).push({});

I would approach this intuitively as follows.

(1.0)(0.1)(0.9)(0.9)=0.081

" (0.1)(0.1)(0.9)=0.009

" (0.1)(0.1)(0.1)=0.001

Sum =0.091

There must be a more efficient and elegant way of doing this but I've not been able to find one. Also, is there a more general formula for a set of n distinct objects each with a probability 1/n of being selected?

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# Probabilities of duplicates

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