What are permutations and combinations?

Permutations and combinations are ways to count how many different groups or orders we can make from a set of items.

Imagine you have 3 toy cars: a red one, a blue one, and a green one. You want to line them up on your bedroom floor.

If the order matters, like when you're racing them, that’s a permutation. For example, red first, then blue, then green is different from green first, then blue, then red. So, you can make 6 different lines with these 3 cars because every swap changes the race!

Now, if the order doesn’t matter, like when you’re just picking a group of friends to play together, that’s a combination. Suppose you have 5 friends and want to pick 2 to join your game. It doesn’t matter who picks first; the group is the same whether it's Alice and Bob or Bob and Alice.

• Permutations are like arranging your toys in different orders, every swap makes a new line.
• Combinations are like choosing a team, the order of choosing doesn’t change who’s on the team.