Final answer:
To find the total number of different outfits, multiply the number of options for hats (3), coats (4), and scarves (2) together, which results in 24 different outfits.
Step-by-step explanation:
The number of different outfits you can select from your closet is determined by the product of the number of choices you have for each type of clothing.
Since you have 3 hats, 4 coats, and 2 scarves, and you need to wear one of each, you simply multiply the number of options for each category together to get the total combinations.
To calculate: Number of combinations = Number of hats × Number of coats × Number of scarves
= 3 × 4 × 2
= 24 different outfits.
The calculation is not a factorial operation, as described in the 4! example for permutations, because factorial refers to the number of ways to arrange a set number of items without repetition.
In this case, we are not arranging but simply combining different elements from each clothing category, so the factorial concept does not apply here.