LESSON: Permutation Probabilities
| Site: | Mountain Heights Academy OER |
| Course: | Introductory Statistics Q4 |
| Book: | LESSON: Permutation Probabilities |
| Printed by: | Guest user |
| Date: | Saturday, 26 April 2025, 12:41 PM |
Finding Probabilities with Permutations - Example 1
You've learned how to calculate permutations now. Remember that permutations keep track of the total number of possible ways to arrange n objects in order.
For example, if I have three paint colors, red, yellow and blue, there are 6 different ways I could choose a paint color for my walls and a different paint color for my ceiling.
Permutations help us keep track of the total number of possibilities when ordering objects. This will come in handy when we're asked to find the probability of a certain order occurring.
For example, what would the probability be of randomly selecting red paint for my walls and yellow paint for my ceiling? There is ONE way to choose red then yellow out of SIX total possibilities. So the probability would be: $$\frac{1}{6} = 16.7%$$.
Watch the following lesson video to review larger permutation calculations and how to use them to find probabilities:
Finding Probabilities with Permutations - Example 2
Sometimes when dealing with permutation calculations, some of the objects may be repeated. That means that two (or more) objects are indistinguishable. When one object is indistinguishable from another that means we over-count the total number of possible permutations. Take a look at the following example so you can see what I mean.
Let's say you have 2 red marbles and 1 blue marble. How many ways can you arrange these marbles in a straight line? There are six ways you can do this!
Notice though, that the red marbles are identical to each other, so even though there are six ways to order those three marbles, only three of those ways are distinguishable.
If asked to calculate a probability using permutations, we need to first make sure we are only counting the distinguishable permutations. Watch the next video to see examples of how to do this correctly.