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###### Daily Dose 034 | Probability and Statistics

#### How do you calculate the probability of Combinations?

Knowing how to calculate the probability of Combinations can be a tricky endeavor.

Often confused with Permutations, without a doubt, come exam day, you are going to see a problem (or problems) that will require you to form subsets of a larger group of items.

So will this be a win for you?

At Prepineer, we are going to make sure that it is.

In this video, we dive into a FE Exam Practice Problem in the subject of PROBABILITY AND STATISTICS, specifically learning how to find the number of COMBINATIONS of given a set of objects.

###### Key Definition

## What is a COMBINATION?

A COMBINATION is a selection of objects where the order doesn’t matter.

For example, say we have three balls: one red, one white, and one blue.

If we wanted to see how many different variations of these balls we get after choosing 2 at a time, we find that we get:

red – white

red – blue

white – blue

white – red

blue – red

blue – white

But since order doesn’t matter, *red – white* and *white – red* are the same.

So that’s a single combination, which goes for the others as well.

So in reality, instead of 6, there are 3 COMBINATIONS.

From a textbook sense, we would first find the number of PERMUTATIONS (which is 6 for the above scenario) and divide it by the number of ways we can rearrange the PERMUTATIONS…meaning, pair them up as white – blue : blue-white, etc.

So if you are wondering…

###### The Process

## How can I calculate the probability of Combinations?

Generally, use the following process to calculate the probability of Combinations.

**Step 1:**Determine the number of items in the sample space (total number of possible outcomes)**Step 2:**Determine the number of items in the event space (the number of outcomes that satisfy the condition of interest)**Step 3:**Use the formula for calculating the number of combinations:**Step 4:**Plug in the values from Steps 1 and 2 into the formula from Step 3 to calculate the number of combinations.**Step 5:**Calculate the probability of the event by dividing the number of combinations by the total number of possible outcomes:P(event) = number of combinations / total number of possible outcomes.

n C r = n! / r!(n-r)!

Where n is the total number of items, r is the number of items in the event space, and ! denotes the factorial function.

Check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, with Love, Prepineer

###### Video Review

## [VIDEO] How to calculate the probability of Combinations?

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