Combinations - Lab

Introduction

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!

Learning objectives

You will be able to:

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

Let's get started

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.

Permutations or Combinations?

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

a. Imagine flatiron school is giving out bronze, silver and gold medal respectively. How many possible ways are there to create this top three?

medal_top_3 = None
medal_top_3

b. Imagine Flatiron school granting the first three contestants a massive fruit basket. How many ways of selecting three people are there in this case?

scholarship_top_3 = None
scholarship_top_3

Some more combinations practice

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.

a. What is the probability that you draw exactly 2 consonants and 3 vowels when drawing 5 letters?

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

b. Out of 6 consonants and 4 vowels, how many words with 2 consonants and 3 vowels can be formed?

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.")

Combinations: creating soccer teams

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

Summary

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.

spikeyball/dsc-1-08-14-combinations-lab-online-ds-sp-000