Editing Birthday problem (section)

====Probability of a unique collision====

The classic birthday problem allows for more than two people to share a particular birthday or for there to be matches on multiple days. The probability that among {{mvar|n}} people there is exactly one pair of individuals with a matching birthday given {{mvar|d}} possible days is<ref name="Pollanen"/>

: <math> p_2(n; d) =   \frac{{n \choose 2}}{d-n+1} (1-p(n; d)) </math>

Unlike the standard birthday problem, as {{mvar|n}} increases the probability reaches a maximum value before decreasing. For example, for {{math|''d'' {{=}} 365}}, the probability of a unique match has a maximum value of 0.3864 occurring when {{math|''n'' {{=}} 28}}.