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Daily Dose 040 | Probability and Statistics
How to identify and solve combinations?
Understanding how to quickly identify and solve combinations was always a challenge for me.
However, there was something one of my instructors had said that really stuck with me, it went something like this:
You should think of Combination locks on our lockers as Permutation locks.
For Combinations, the order DOES NOT MATTER.
For Permutations, the order DOES MATTER.
So with this, if our code was 7 21 1 to open our locker, if it was a true Combination lock, then we could put in those numbers in any order!
But they need to be put in that exact order to open, therefore, ORDER MATTERS and it is a Permutation lock! 🙂
For some reason, that always stuck with me.
In this video, we break it all down, showing you exactly how to go about identify and solve combinations faster and with a lot less stress on the FE Exam.
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.
This 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.
The Process
How can we identify and solve Combinations fast?
To biggest factor in solving a Combination problem fast is having a keen ability in identifying them as you are reading through a problem statement – the first time.
Here are some tips:
- Keywords
- Order vs. Selection
- Repetition
- Grouping
- Problem Context
Look for specific keywords that indicate combinations or permutations. For combinations, words like “select,” “choose,” “combination,” or “group” are often used. For permutations, words like “arrange,” “order,” “sequence,” or “permute” may be present.
Determine if the order of the items matters or not. In permutations, the order of the selected items is important, whereas in combinations, the order does not matter.
Check if the problem allows repetition of items. If the problem allows repeated items, it is more likely a permutation problem. If repetition is not allowed, it could be a combination problem.
Consider whether the problem involves forming groups or subsets from a larger set. If the problem asks for the number of ways to select a group of items without considering their order, it is likely a combination problem.
Consider the context of the problem and the nature of the objects or items involved. Are you selecting items from a set without regard to order, or are you arranging objects in a particular order?
Knowing what keywords and clues to be looking for will be the determinate in whether or not you are able to identify and solve combinations fast.
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
