# Binomial coefficient

JavaScript, Math, Algorithm · Dec 28, 2020

Calculates the number of ways to choose `k`

items from `n`

items without repetition and without order.

- Use
`Number.isNaN()`

to check if any of the two values is`NaN`

. - Check if
`k`

is less than`0`

, greater than or equal to`n`

, equal to`1`

or`n - 1`

and return the appropriate result. - Check if
`n - k`

is less than`k`

and switch their values accordingly. - Loop from
`2`

through`k`

and calculate the binomial coefficient. - Use
`Math.round()`

to account for rounding errors in the calculation.

const binomialCoefficient = (n, k) => { if (Number.isNaN(n) || Number.isNaN(k)) return NaN; if (k < 0 || k > n) return 0; if (k === 0 || k === n) return 1; if (k === 1 || k === n - 1) return n; if (n - k < k) k = n - k; let res = n; for (let j = 2; j <= k; j++) res *= (n - j + 1) / j; return Math.round(res); }; binomialCoefficient(8, 2); // 28