We make choices every day.
When you choose what pants to match with what shirt, you're choosing a combination.
When you're getting food, and you choose a main dish, and two sides, you're choosing a combination.
Combinations are like pairs that we choose from different groups.
Math people will get a little more fancy, and tell you:
Combinations are selections of items from two or more sets. The order of the items does not matter. 🥸
Let's say you go to an ice cream store.
You can choose between vanilla and chocolate ice cream.
For the toppings, you can choose between sprinkles and strawberries.
How many possible combinations can you make with the ice cream and toppings?
You can create a grid to list all the possible combinations:
There are 4 rows, which means there are 4 possible combinations.
You can also make a tree diagram.
There are 4 leaves (if you think of the lines like branches), which also means there are 4 possible combinations.
A quick way to count combinations is with multiplication.
There are 2 ice cream flavors and 2 kinds of toppings.
Let's multiply them. 👇
2 × 2 = 4
We get 4 combinations!
This is the same answer we got when we used the grid and the tree diagram.
But solving it with multiplication is quicker. 😎
Let's say a girl named Sally is buying some new clothes at the store. She wants a shirt and a skirt.
For the shirt's color, she can pick blue, yellow, or green.
For the skirt's design, she can choose either plain or checkered.
How many combinations can Sally choose from? 🤔
👉 We know the quickest way is to multiply. 🏎
There are 3 shirt colors and 2 skirt designs.
We multiply these numbers to get the total number of combinations.
3 x 2 = 6
There are 6 different combinations.
Let's check our answer using a tree diagram.
The list in the diagram shows 6 different combinations, or pairs.
Let's try to see if it matches what we list in a grid.
There are 6 rows of unique shirt-skirt pairs, which also shows there are 6 combinations!
Great work learning about combinations. 👏
Now, try the practice. You'll understand more and remember for longer.