## Mathematical Combinations

The combination formula is this…

with *n* being the number of items available to you and *k* the number of items you can pick at one time (where order does not matter).

In other words, if *n* = 4 (a,b,c,d), and *k* = 2, it means that we have four items to choose from, and we can only choose two at a time. So the different combinations would be…

a b a c a d b c b d c d

Because order does not matter (`a b`

is the same thing as `b a`

) we have a total of 6 possible unique combinations.

## Factorials in Python

To calculate the number of combinations we need to use factorials (the *!* symbol).

Factorials work like this…

3! = 3 x 2 x 1 = 6 4! = 4 x 3 x 2 x 1 = 24 5! = 5 x 4 x 3 x 2 x 1 = 120 ... and so on.

In python, factorials can be found in the `math`

module

from math import factorial

…and can be used like this.

>>> factorial(6) 720

## Python Combination Function

the function looks like this

def combination(n,k): numerator=factorial(n) denominator=(factorial(k)*factorial(n-k)) answer=numerator/denominator return answer

So if we run the function with the above example (*n*=4 and *k*=2), we should get the right answer.

>>> combination(4,2) 6

DONE!