Question

Suppose that there are 3 hats, 2 coats, and S scarves in your closet. Assuming you are comfortable with wearing any combination of hat, coat, and scarf, and you need a hat, a coat, and a scarf, you have 3 choices for the hat, 2 choices for the coat, and S choices for the scarf. Therefore, the total number of different outfits you can create is 3 * 2 * S = 6S.

Answer 1

The question focuses on the mathematical concept of combinations, where the total number of outfits is determined by multiplying the number of choices for hats, coats, and scarves, resulting in an equation of 6S combinations.

Step-by-step explanation:

The question refers to the concept of combinations and how to calculate the total number of outfit combinations one can create using various items of clothing, given a certain number of hats, coats, and scarves. The principle of counting combinations here is similar to calculating a factorial, such as 4!, which is an arrangement of 4 items in all possible ways (4×3×2×1). However, for the given problem with multiple categories of items (hats, coats, scarves), we use the product rule of counting, which says if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the two events can occur in 'm × n' ways. Therefore, if we have 3 hats, 2 coats, and S scarves, the total number of different outfits one can create is calculated as the product of these independent choices: 3 (hats) × 2 (coats) × S (scarves) = 6S. This equation represents the fundamental principle of counting different combinations.