Editing Birthday problem (section)

===Near matches===
Another generalization is to ask for the probability of finding at least one pair in a group of {{mvar|n}} people with birthdays within {{mvar|k}} calendar days of each other, if there are {{mvar|d}} equally likely birthdays.<ref name="abramson">M. Abramson and W. O. J. Moser (1970) ''More Birthday Surprises'', [[American Mathematical Monthly]] '''77''', 856–858</ref>

:<math> \begin{align} p(n,k,d) &= 1 - \frac{ (d - nk -1)! }{ d^{n-1} \bigl(d - n(k+1)\bigr)!}\end{align} </math>

The number of people required so that the probability that some pair will have a birthday separated by {{mvar|k}} days or fewer will be higher than 50% is given in the following table:

:{| class="wikitable" style="text-align: center"
! {{mvar|''k''}} !! {{mvar|n}}<br />for {{math|''d'' {{=}} 365}}
|-
|0 || 23
|-
|1 || 14
|-
|2 || 11
|-
|3 || 9
|-
|4 || 8
|-
|5 || 8
|-
|6 || 7
|-
|7 || 7
|}

Thus in a group of just seven random people, it is more likely than not that two of them will have a birthday within a week of each other.<ref name="abramson"/>