# Permutatations vs variations vs combinations

1 when to choose what. Please explain with an example. In a layman words what would be the difference between these. Please explain differences with more examples

Hey Pratap,

Thank you for reaching out!

The final lecture of this section, Summary of Combinatorics, summarizes all three concepts:

https://learn.365datascience.com/courses/probability/summary-of-combinatorics/

Additionally, you can refer to the answer in the followig thread:

https://365datascience.com/q/c09ec0acb3

Kind regards,

365 Hristina

Permutations:

Layman Explanation: Think of permutations as different "line-ups". Imagine you're lining up for a photo, and every different order of people in that line results in a different photo.

When to use: When the order of items matters.

Example: You're choosing the 1st, 2nd, and 3rd place winners from a race with 10 participants. The person who comes first is distinct from the one who comes second or third.

Using 10 runners: The number of ways to choose 1st, 2nd, and 3rd places is given by permutations of 10 items taken 3 at a time.

Variations:

Layman Explanation: This is a bit trickier. Variations are like permutations but with a twist. Imagine you have 10 books, but you're only choosing 3 to take on a trip. Each different order you can pack these books is a variation.

When to use: When you're not using all items, but the order of the ones you're using still matters.

Example: Out of 10 books on your shelf, you want to pack 3 in your bag. If the order in which you read them matters (e.g., a three-part series), then the number of ways to pack them in order is given by variations of 10 items taken 3 at a time.

(It's worth noting that, mathematically, permutations and variations overlap when you're choosing a subset of items in order. So, the formulas for them coincide in this scenario.)

Combinations:

Layman Explanation: Combinations are like making "groups" without caring about the order inside the group. Imagine you're making a team; it doesn't matter who joined the team first or last, just who's on the team.

When to use: When you're selecting items, and the order doesn't matter.

Example: Out of 10 friends, you want to invite 3 to watch a movie. It doesn't matter in which order you call them; you just want them there. The number of ways to choose your 3 friends is given by combinations of 10 items taken 3 at a time.

More Examples:

Permutations: Think about the different ways numbers can be arranged in a lottery draw. If you have a lottery where you pick 5 numbers out of 50, and the order matters, that's permutations.

Variations: Imagine picking 3 different toppings for a pizza from a list of 10. The order in which they're added could change the taste slightly (first cheese, then olives, then peppers vs. first olives, then cheese, then peppers).

Combinations: Consider making a fruit salad using 3 fruits out of 7 available. Whether you picked apples first, oranges second, and bananas third, or bananas first, apples second, and oranges third, you'd still have the same three fruits in the salad.

Remember:

Permutations = specific line-ups or orders.

Variations = specific line-ups from a subset.

Combinations = groups, without caring about the order inside.