Now, let's dive into combinations. In the previous lab, we saw how the order was important. Cracking a code is one example, but what if the order doesn't matter, for example, when an engaged couple want to pick 3 wedding cakes from a list of 15? You'll need to use another technique here, and this is where combinations come in handy!

You will be able to:

• Practice how to use combinations when the order is not important
• Create (easy) functions for combinations and permutations

From the previous lab, you remember that we created a factorial function like this.

Now, let's use this factorial function to create a function combination as well as permutation, both holding 2 arguments n and k.

def factorial(n):
    prod = 1
    while n >= 1:
        prod = prod * n
        n = n - 1
    return prod

def permutation(n,k):
    None

def combination(n,k):
    None

Great! We can use these functions in the following exercises.

Flatiron School is holding a mini mathematics contest, and there are 9 people in the last round.

medal_top_3 = None
medal_top_3

scholarship_top_3 = None
scholarship_top_3

Imagine you have 6 consonants and 4 vowels witten on a pieces of paper in a bag. You'll draw 5 letters out of the bag.

Write the code for getting total number of ways of drawing 2 out of 6 and 3 out of 4 below

draw_cons = None
draw_vow = None

The total number of ways to draw 5 letters out of 10 letters.

sample = None

The probability of drawing 2 consonants and 3 vowels when drawing 5 letters:

None

You can reuse a part of the previous exercise. Which part? print the result below.

draw_cons = None
draw_vow = None

Now we need to take into account that order is important.

order_5_letters = None

The total number of words with 2 consonants and 3 vowels then equals:

total_words = None
print("In total,",  total_words, "words with 2 consonants and 3 vowels can be formed from our existing letter pool.")

We're holding a mini soccer tournament and 16 people are participating. We'd like to form 4 teams of 4. How many ways are there to do this?

None

None  # the answer is 2627625.0

In this lab, you got some practice on combinations! Congrats, combinations and permutations are the cornerstones of combinatorics, and you now know how to use them in various settings.