Implementing Permutations and Combinations (#481)

* calculates the number of permutations and combinations

* calculates the number of permutations and combinations

* calculates the number of permutations and combinations

* updating DIRECTORY.md

* calculates the number of permutations and combinations

* calculates the number of permutations and combinations

* fixed a typo

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -115,6 +115,7 @@
   * [PerfectCube](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PerfectCube.js)
   * [PerfectNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PerfectNumber.js)
   * [PerfectSquare](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PerfectSquare.js)
+  * [PermutationAndCombination](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PermutationAndCombination.js)
   * [PiApproximationMonteCarlo](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PiApproximationMonteCarlo.js)
   * [Polynomial](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Polynomial.js)
   * [PrimeCheck](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/PrimeCheck.js)

Maths/PermutationAndCombination.js

@@ -0,0 +1,67 @@
+/**
+ * @details Calculates the number of permutations and combinations.
+ * @external_link (Permutation And Combinations)[https://www.geeksforgeeks.org/permutation-and-combination/]
+ */
+
+/**
+ * @brief Calculates the factorial of the given number.
+ * @param num: integer
+ * @details Factorial of n = n * (n - 1) * (n - 2) * ... * 1
+ * @returns integer: Factorial of the number.
+            NaN: if negative number is provided.
+ */
+const factorial = (n) => {
+  if (n >= 0) {
+    if (n === 0) {
+      return 1
+    } else {
+      return n * factorial(n - 1)
+    }
+  } else {
+    return NaN
+  }
+}
+
+/**
+ * @brief Calculates the number of Permutations from the given data.
+ * @param
+ * n: integer -> number of items.
+ * r: integer -> number of times n is taken.
+ * @returns integer: The number of permutations.
+            NaN: if negative number is provided.
+ */
+const permutation = (n, r) => {
+  return factorial(n) / factorial(n - r)
+}
+
+/**
+ * @brief Calculates the number of Combinations from the given data.
+ * @param
+ * n -> number of items.
+ * r -> number of times n is taken.
+ * @returns integer: The number of combinations.
+            NaN: if negative number is provided.
+ */
+const combination = (n, r) => {
+  return factorial(n) / (factorial(r) * factorial(n - r))
+}
+
+// Exports the functions to be used in other files.
+module.exports.factorial = factorial
+module.exports.permutation = permutation
+module.exports.combination = combination
+
+/**
+ * @example
+
+   const funcs = require("./PermutationAndCombination.js");
+
+   console.log(funcs.factorial(5));
+   console.log(funcs.permutation(5, 2));
+   console.log(funcs.combination(5, 2));
+
+ * @output
+   120
+   20
+   10
+ */