Editing Birthday problem (section)

==== Number of days with at least two birthdays ====
The above can be generalized from the distribution of the number of people with their birthday on any particular day, which is a [[Binomial distribution]] with probability {{math|{{sfrac|1|''d''}}}}. Multiplying the relevant probability by {{mvar|d}} will then give the expected number of days. For example, the expected number of days which are shared; i.e. which are at least two (i.e. not zero and not one) people's birthday is:

<math display="block">d - d \left (\frac {d-1} {d} \right )^n - d \cdot \binom{n}{1} \left (\frac {1} {d} \right )^1\left (\frac {d-1} {d} \right )^{n-1} = d - d \left (\frac {d-1} {d} \right )^n - n \left (\frac {d-1} {d} \right )^{n-1} </math>