The following are the common definitions of Binomial Coefficients.
A binomial coefficient C(n, k) can be defined as the coefficient of x^k in the expansion of (1 + x)^n. Binomial coefficient C(n, k) also gives the number of ways, disregarding order, that k objects can be chosen from among n objects more formally, the number of k-element subsets (or k-combinations) of an n-element set.
Problem Statement: Write a function that takes two parameters n and k and returns the value of Binomial Coefficient C(n, k). For example, your function should return 6 for n = 4 and k = 2, and it should return 10 for n = 5 and k = 2.
Approach: Below are the steps to be followed in order to create a function that returns the binomial coefficient of two integers.
- Create a function that takes to arguments n and k.
- Now check whether the n and k are numbers. If both or one of them are not numbers then return NaN.
- Now check if k is less than 0 or k is greater than n. If one of the statements is true then return 0.
- Now check if the k is equal to 1 or k is equal to n. If one of the statements is true then return 1.
- Now check if k is equal to 1 or k is equal to (n-1). If one of the statements is true then return n.
- Now write the logic to get the binomial coefficient.
Example: This example shows the above-explained approach.
Javascript
<script>     function binomialCoefficient (n, k){             // Checking if n and k are integer       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       }             let res = n;       for(let i = 2; i <= k; i++){         res *= (n - i + 1) / i;       }             return Math.round(res);     }           console.log(binomialCoefficient(10, 2)) </script> |
Output:
45
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