(199/200)^200 * [1 - binomcdf(200, 1/200, 5)] ≈ 1 in 4832
where binomcdf is the
Binomial distribution's cumulative distribution function. A TI graphing calculator calls it binomcdf(); spreadsheet software calls it binomdist().
The combinations represent arrangements of two symbols: there are C(5,2) ways to arrange AAABB, for instance.