Add factorial.

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)