Editing Birthday problem (section)

===Number of people who repeat a birthday===
The probability that the {{mvar|k}}th integer randomly chosen from {{math|[1,''d'']}} will repeat at least one previous choice equals {{math|''q''(''k'' − 1; ''d'')}} above. The expected total number of times a selection will repeat a previous selection as {{mvar|n}} such integers are chosen equals<ref>{{cite web|last1=Might|first1=Matt|title=Collision hash collisions with the birthday paradox|url=http://matt.might.net/articles/counting-hash-collisions/|website=Matt Might's blog|access-date=17 July 2015}}</ref>

:<math>\sum_{k=1}^n q(k-1;d) = n - d + d \left (\frac {d-1} {d} \right )^n</math>
This can be seen to equal the number of people minus the expected number of different birthdays.