Math Problem Statement

A girl has 4 skirts, 7 blouses, and 7 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear? (Assume that each item matches all the others, so she is willing to wear any combination.)

Solution

To find the total number of different outfits the girl can wear, we can use the fundamental principle of counting. Since each item matches the others, each choice is independent, and we multiply the number of choices for each item:

  1. Skirts: She has 4 options.
  2. Blouses: She has 7 options.
  3. Shoes: She has 7 options.

So, the total number of unique outfits she can create is: 4×7×7=1964 \times 7 \times 7 = 196

Thus, she can wear 196 different skirt-blouse-shoe combinations.

Would you like a breakdown of similar counting principles, or do you have any more questions?

Here are some related questions:

  1. What if she had 5 skirts instead of 4?
  2. How would the total combinations change if one blouse didn’t match one of the skirts?
  3. What is the probability she chooses a specific skirt-blouse-shoe combination if she picks randomly?
  4. How many combinations would there be if she only had 3 pairs of shoes?
  5. If she can add one more item (like a jacket), how many outfits can she create?

Tip: When solving counting problems, always identify independent choices and multiply their quantities.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Counting Principle

Formulas

Total combinations = number of skirts × number of blouses × number of shoes

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grades 5-7