When we talk about combinations in the English language, we have a problem. People regularly use the word “combination” when that isn’t what they mean at all. Combinations are a collection of things when the order DOES NOT matter. Choosing which 3 stuff animals out of a collection of 10 to take with you on a trip is an example of a combination. A combination lock is a great example of using the word incorrectly. The order of the numbers matters in order to open the lock. When the order matters, that is called a permutation.
Another great way to look at this can be through sports. If a basketball coach needs to pick his starting line-up from a team of 8 players, he can have any combination of 5 of the players. Whatever order the players are selected, it is still the same group of 5 starting players for the line-up. When a baseball coach is deciding the batting order, the order of the players matters. The baseball example has to be a permutation.
Combination Activity with Dress-up Clothing:
I had my son select 3 dress-up hats and 2 weapons. We then had a photo-shoot of him with the different combinations that he could have (assuming he has to have a hat and a weapon). There are six different possibilities.
If we also can have no hat and no weapon OR just one of each, that adds another 6 combinations.
Permutation Activity with Play Animals in a Zoo:
In this example, we are going to use 3 animals to show the different permutations of the animals in cages at the zoo. The order that we put the animals in their cages matters, so this a permutation. (Other variations of the same idea would be having 3 children sit on 3 chairs or putting stuffed animals in order.)
With our 3 animals, we have a total of 6 different permutations. If we have 4 animals, we would have 24 different permutations. Permutations can become large very quickly!
I hope this helps you understand the difference between combinations and permutations and that you can have fun with these ideas with your children. Please let me know if you have any questions about this!