Math Problem Statement

When you get ready to get dressed for school you open your closet to find that you have the following choices: there are 4 clean shirts in your closet; you can also choose between jeans, sweatpants, khakis, or shorts; then for your feet you can choose tennis shoes or sandals. You decide tennis shoes would be better than sandals. How many different outfits could be made with the shirt and pant options?

Solution

To determine how many different outfits you could make with your shirt and pant options, let's break it down step by step:

  1. Shirts: You have 4 clean shirts to choose from.
  2. Pants: You can choose between jeans, sweatpants, khakis, or shorts, which gives you 4 options for pants.
  3. Shoes: You've already decided to wear tennis shoes, so there’s only 1 option for shoes.

Now, multiply the number of choices for each clothing category:

Total outfits=(Number of shirts)×(Number of pants)×(Number of shoes)\text{Total outfits} = (\text{Number of shirts}) \times (\text{Number of pants}) \times (\text{Number of shoes})

Substitute the values:

Total outfits=4×4×1=16\text{Total outfits} = 4 \times 4 \times 1 = 16

So, you can make 16 different outfits with your available shirts, pants, and tennis shoes.

Would you like more details on the calculation, or have any questions?

Here are 5 related questions you might find interesting:

  1. What if you had 5 shirts instead of 4? How many outfits could you make then?
  2. How would the total change if you considered both tennis shoes and sandals as options?
  3. If you added jackets as another category of clothing, how would you calculate the new total?
  4. What if you wore a uniform with only 1 shirt and 1 pant choice? How many outfits would be possible then?
  5. How many outfits could you make if each day you could wear either shorts or pants but not both?

Tip: Always multiply the number of choices from each category to find the total combinations.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication principle of counting

Formulas

Total outfits = (Number of shirts) × (Number of pants) × (Number of shoes)

Theorems

Fundamental Counting Principle

Suitable Grade Level

Grades 4-6