log(multinomial coefficient) from logs all the way down
npm install multinomial-ln
var multinomialLn = require('multinomial-ln')
Math.round(Math.exp(multinomialLn([3, 5, 3, 5, 5]))
// 821292151680You can also work completely in log.
multinomialLn([1, 5, 7, 5, 5, 1, 2, 3])
// 106.60573852903470As the factorial function used to generate these log-multinomial coefficients is approximate, results like this one are not exact, although respecting the magnitude of this value (e^106.6), the actual value is plenty close. Keep this in mind.
Multinomial coefficients can quickly become huge, even for small counts and small numbers of terms. This makes the impossible to compute without a bit of cleverness. For example, the multinomial coefficient for [ 6, 4, 5, 3, 3 ] will overflow the vanilla node multinomial coefficient library. Where exact results are not required (a big number library is not required to calculate these) they can be generated using log terms for the factorials that underly them. That is what this library implements. As such it is probably most-useful in projects focused on probabilities and statistics.
MIT