Combinations Formula: Explantation and Example
Doing mathematic problems where the order of the items in a list doesn’t matter involves using the combination formula. In mathematics, specifically statistics, there are various ways for you to understand the number of combinations in a set. In fact, you can even use different types of mental math tricks to figure out simple combination.
For more complex situations that involves groups of people in the dozens or hundreds, the combination formula is a necessity. You can learn tons of math skills from the Udemy course Easy Advanced Math Skills offered, and they use formulas like the one for combination to help make your work easier.
What is a Combination Formula?
Above is the combination formula in full detail. The combination formula features two prominent variables. The combinations are decided using r, which are random objects, and n, which are distinct or specific objects. The order of the objects doesn’t matter, but the overall problem itself.
There are also a number of factorial problems involved, these are the problems that look like so: n! or r!(n –r)!.
The factorial is a short way to write a large number of consecutive numbers that are positive. For example, 3! Would equal out to being 3 * (3 -1) * (3 – 1 – 1), until you reach the number 1. Remember that the factorial of 0 or 0! is always equal to 1.
The second half of the equation is broken down by dividing the number of distinct numbers or n by the number of random objects also known as r. The problems that require you to find the combination of numbers is usually represented as nCr.
An Example of Using the Combination Formula
An example of a combination problem that uses the combination formula is how many different groups of 7 items can be found if you take 4 items at a time. Remember, the combination of the items doesn’t matter, and there is no specific order that is involved in the combination.
The problem would be written out like so – 7C4 – and it is put into the formula that was mentioned above as 7!/3!4!. Remember that the formula is set up as 7! The number of items in a group, also known as n and r, which is the number of items that you take away from the group at one time as a whole.
The formula subtracts the number from the group (n-r)! and multiplies it by the group of numbers that are taking for each combination, again, which is known as r.
So the equation n!/(n-r)!r! for this particular equation equals out to 7!/3!4!
This is a huge equation to work out on your own, but there’s a simple way to fix it and reduce it to a much easier problem.
Break down 7! Into the following equation 7* 6 * 5 * 4! / 3 * 2 * 1 * 4! Now all you have to do is divide the two 4 factorials away from each other and you are just left with the remaining.
Multiplying 7 * 6 * 5/ 3 * 2 * 1 is definitely a lot easier than the alternative, and you can calculate the answer with mental math. You should get 35. Although the numbers are large, note how the number of combinations is relatively small.
These are the type of problems you will fact when doing statistics. The Udemy course Practical Statistics for the user Experience gives you a lesson in other forms of statistics and how you may run into problems like this in the real world.
What Do You Use the Combination Formula For?
Getting the combination of various groups using numerical data is a useful way to various jobs. Many accounting and financial jobs that involve doing statistical calculations make use of both the combination and permutation formulas in order for people to come up with concrete answers on complex problems. The combination problems can be used to help do statistics on certain groups of people, to find the maximum number of combinations you can get with various objects, or to help you group people together with specific attributes.
All of these are an aspect of financial math and Udemy has a great course titled Fundamental Financial Math that teaches you about the basic forms of math you have to do for finances. You can also check out the Udemy course Introductory Statistics to learn about the basics of statistics and how to implement it through various problems and exercises.
Last Updated January 2022
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