Saturday Serendipity
Quote,Mental model, Interesting find.
Hi there!
Reading time : About 5 minutes
Quote
"The beauty of it is that knowledge is cumulative. And even what you're learning about Company A will help you thinking about Company B." ~ Warren Buffett
Mental Model
Permutations and Combinations
I have always hated permutations and combinations. But like everything that I have hated in physics, chemistry, biology and mathematics; Munger comes up and says it’s important to have the big ideas from all the disciplines. He said Permutations and Combinations is one of the most important concepts in understanding the world.
So here is my humble attempt to try and explain how this mental model can be used to understand the world and how it can help us in making decisions.
“If you don’t get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one legged man in an ass kicking contest. You’re giving a huge advantage to everybody else.” Munger
After all who wants to be a one legged man in an ass kicking contest.
Not me.
Let’s start with a simple example. Let’s say you want to make tea.
First we need the ingredients so you will need chai patti, sugar, milk, water, adrak. But you can use other products also. (oat milk, brown sugar, stevia, etc.) Now this is a combination problem. You have to decide which ingredients you have to put in. Let’s say you have done that and put all of these ingredients in the order listed. What’s going to happen is the chai will taste bad. Why?
The order you put the ingredients in was wrong.
For someone who knows how to make chai, they know that you have to put water first then chai patti then adrak then the milk and then the sugar. It is all about the order. Here even the permutations matter.
This is an oversimplification maybe but understand that permutations is all about the order and combinations is all about the groups.(order doesn’t matter)
For that matter a combination lock should really be called a permutation lock. The order you put the numbers in matters. A true combination lock would accept both 10-17-23 and 23-17-10 as correct.
In Cricket
Now let’s say you are the captain of a cricket team. You have 15 players.This team includes five batsmen, four bowlers, three all-rounders, two wicket-keepers, and one captain. The captain needs to choose an opening pair of two batsmen for a crucial match. To calculate the number of possible opening pairs, we use permutations. The formula for permutations is P(n, r) = n! / (n-r)!, where "n" is the total number of items (in this case, five batsmen), and "r" is the number of items chosen (in this case, two batsmen for the opening pair).
P(5, 2) =(5 × 4 × 3 × 2 × 1) / (3 × 2 × 1) = 120 / 6 = 20
Or the harder version of the formula
P(5,2)= 5! / (5-2)! = 5! / 3! = 5 * 4 = 20
So, there are 20 different combinations of two batsmen that the captain can choose for the opening pair out of the five available batsmen. You have permutations and combinations as a cricketer and you don’t even know about it! It’s crazy. It is very important to have the right pair of batsmen to open the batting because if you mess it up and there are two individuals who are good but together not that good your team suffers. So when you make a decision you have to make one which is considering all options.
In Investing
When it comes to a creation of a portfolio it is all about permutations and combinations. Let's say an investor wants to create a diversified portfolio by investing in a combination of five different stocks out of a pool of ten potential stocks. To calculate the number of possible portfolios, we use combinations. The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where "n" is the total number of items (in this case, ten potential stocks), and "r" is the number of items chosen (in this case, five stocks).
C(10, 5) = 10! / (5! * (10-5)!) = 252
So, there are 252 different ways the investor can create a portfolio by selecting five stocks out of the ten available options.
This is crazy!
Conclusion
Obviously, you’ve got to be able to handle numbers and quantities—basic arithmetic. And the great useful model, after compound interest, is the elementary math of permutations and combinations. And that was taught in my day in the sophomore year in high school…It’s very simple algebra. It was all worked out in the course of about one year between Pascal and Fermat. They worked it out casually in a series of letters.
It’s not that hard to learn. What is hard is to get so you use it routinely almost everyday of your life. The Fermat/Pascal system is dramatically consonant with the way that the world works. And it’s fundamental truth. So you simply have to have the technique.
If you don’t get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one legged man in an asskicking contest. You’re giving a huge advantage to everybody else.
One of the advantages of a fellow like Buffett, whom I’ve worked with all these years, is that he automatically thinks in terms of decision trees and the elementary math of permutations and combinations. ~ Charlie Munger
I think his words on the importance of this mental model are good enough for you to give it a try in understanding. I am trying to learn a bit more about it as well and writing this has helped. A great source is this book Zero I haven’t started reading it but have added it to my list based off a recommendation. Maybe you can aswell.
Interesting find
That’s it for this week!
Enjoy the weekend! Happy learning.