There are 2 hats, 3 scarves, and 3 pairs of mittens
How many different combinations of 1 hat, 1 scarf, and 1 pair of mittens?
How would I solve this, other than writing out each combination?
Could someone please explain how?
2*3*3 = 18
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To solve this problem without writing out each combination, you can use the concept of permutations.
Here's how you can approach it step-by-step:
Step 1: Count the number of options for each item.
In this case, there are 2 options for hats, 3 options for scarves, and 3 options for pairs of mittens.
Step 2: Multiply the number of options for each item together.
Since you need to choose 1 hat, 1 scarf, and 1 pair of mittens, you multiply the number of options for each item together:
2 (hats) * 3 (scarves) * 3 (pairs of mittens) = 18
Therefore, there are 18 different combinations of 1 hat, 1 scarf, and 1 pair of mittens.
Using the concept of permutations saves you from writing out each combination and helps you find the total number directly.
To solve this problem efficiently, you can use a basic principle of counting called the multiplication principle. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things together.
In this case, you have 2 hats, 3 scarves, and 3 pairs of mittens. To find the number of different combinations of 1 hat, 1 scarf, and 1 pair of mittens, you can multiply the number of options for each item:
Number of hat options: 2
Number of scarf options: 3
Number of mitten options: 3
Using the multiplication principle, you can multiply these numbers together:
2 * 3 * 3 = 18
So, there are 18 different combinations of 1 hat, 1 scarf, and 1 pair of mittens.
Instead of writing out each combination, you can use the multiplication principle to calculate the total number of combinations quickly.