Add factorial.

Author: trekhleb

README.md

@@ -28,6 +28,7 @@
 ### Algorithms
 
 * **Math**
+  * [Factorial](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
   * [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
   * [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/cartesian-product)
   * [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
@@ -37,7 +38,7 @@
   * [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
 * **String**
   * [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/permutations) (with and without repetitions)
-  * Combination
+  * [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/combinations) (with and without repetitions)
   * Minimum Edit distance (Levenshtein Distance)
   * Hamming
   * Huffman

src/algorithms/math/factorial/README.md

@@ -0,0 +1,32 @@
+# Factorial
+
+In mathematics, the factorial of a non-negative integer `n`, 
+denoted by `n!`, is the product of all positive integers less 
+than or equal to `n`. For example:
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n     | n!                          | 
+| ----- | :-------------------------: |
+| 0     | 1                           |
+| 1     | 1                           |
+| 2     | 2                           |
+| 3     | 6                           |
+| 4     | 24                          |
+| 5     | 120                         |
+| 6     | 720                         |
+| 7     | 5 040                       |
+| 8     | 40 320                      |
+| 9     | 362 880                     |
+| 10    | 3 628 800                   |
+| 11    | 39 916 800                  |
+| 12    | 479 001 600                 |
+| 13    | 6 227 020 800               |
+| 14    | 87 178 291 200              |
+| 15    | 1 307 674 368 000           |
+
+## References
+
+[Wikipedia](https://en.wikipedia.org/wiki/Factorial)

src/algorithms/math/factorial/__test__/factorial.test.js

@@ -0,0 +1,11 @@
+import factorial from '../factorial';
+
+describe('factorial', () => {
+  it('should calculate factorial', () => {
+    expect(factorial(0)).toBe(1);
+    expect(factorial(1)).toBe(1);
+    expect(factorial(5)).toBe(120);
+    expect(factorial(8)).toBe(40320);
+    expect(factorial(10)).toBe(3628800);
+  });
+});

src/algorithms/math/factorial/factorial.js

@@ -0,0 +1,13 @@
+/**
+ * @param {number} number
+ * @return {number}
+ */
+export default function factorial(number) {
+  let result = 1;
+
+  for (let i = 1; i <= number; i += 1) {
+    result *= i;
+  }
+
+  return result;
+}

src/algorithms/string/combinations/README.md

@@ -11,8 +11,45 @@ its the same fruit salad.
 
 ## Combinations without repetitions
 
+This is how lotteries work. The numbers are drawn one at a 
+time, and if we have the lucky numbers (no matter what order) 
+we win!
+
+No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
+
+**Number of combinations**
+
+![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-no-repeat.png)
+
+where `n` is the number of things to choose from, and we choose `r` of them,
+no repetition, order doesn't matter.
+
+It is often called "n choose r" (such as "16 choose 3"). And is also known as the Binomial Coefficient.
+
 ## Combinations with repetitions
 
+Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
+
+Or let us say there are five flavours of icecream: 
+`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
+
+We can have three scoops. How many variations will there be?
+
+Let's use letters for the flavours: `{b, c, l, s, v}`. 
+Example selections include:
+
+- `{c, c, c}` (3 scoops of chocolate)
+- `{b, l, v}` (one each of banana, lemon and vanilla)
+- `{b, v, v}` (one of banana, two of vanilla)
+
+**Number of combinations**
+
+![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif)
+
+Where `n` is the number of things to choose from, and we 
+choose `r` of them. Repetition allowed, 
+order doesn't matter.
+
 ## References
 
 [Math Is Fun](https://www.mathsisfun.com/combinatorics/combinations-permutations.html)