hipergeometric function in javascript (with some testcases)

hipergeometic.js

//07.11.2023

// Factorial function
const fact = (x) => (x == 0 ? 1 : x * fact(x - 1));

// binomial coefficient where a is the total set of posibbilites and b is the number of combinatios we're interested in
const bincoeff = (a, b) => fact(a) / (fact(a - b) * fact(b));

//hipergeometric function
const hipergeo = (M, N, n, k) => (bincoeff(M, k) * bincoeff(N - M, n - k)) / bincoeff(N, n);

//example : calc prob >= 3
let N = 164, M = 18, n = 25, probabilidadeSum = 0.0;
for (let k = 3; k < 18; k++) {
    probabilidadeSum += hipergeo(M, N, n, k);
}
console.log("Probabilidade = ", probabilidadeSum);

//use case, german lotto: 
console.log(hipergeo(6, 49, 6, 0)); //lotto DE, 0 ok
console.log(hipergeo(6, 49, 6, 1)); //lotto DE, 1 ok
console.log(hipergeo(6, 49, 6, 2)); //lotto DE, 2 ok
console.log(hipergeo(6, 49, 6, 3)); //lotto DE, 3 ok
console.log(hipergeo(6, 49, 6, 4)); //lotto DE, 4 ok
console.log(hipergeo(6, 49, 6, 5)); //lotto DE, 5 ok
console.log(hipergeo(6, 49, 6, 6)); //lotto DE, 6 ok

//with      layback: https://de.wikipedia.org/wiki/Binomialverteilung
//without   layback: https://de.wikipedia.org/wiki/Hypergeometrische_Verteilung