Questions: Juan owns 6 pairs of pants, 3 shirts, 5 ties, and 3 jackets. How many different outfits can he wear to school if he must wear one of each item? 17 270 18 15 None of the above SUBMIT

Juan owns 6 pairs of pants, 3 shirts, 5 ties, and 3 jackets. How many different outfits can he wear to school if he must wear one of each item? 17 270 18 15 None of the above SUBMIT
Transcript text: Juan owns 6 pairs of pants, 3 shirts, 5 ties, and 3 jackets. How many different outfits can he wear to school if he must wear one of each item? 17 270 18 15 None of the above SUBMIT
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Solution

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Solution Steps

To determine the number of different outfits Juan can wear, we need to calculate the product of the number of choices he has for each clothing item. Since he must wear one of each item, we multiply the number of pants, shirts, ties, and jackets together.

Step 1: Determine the Number of Choices for Each Clothing Item

Juan has the following number of choices for each clothing item:

  • Pants: 6 choices
  • Shirts: 3 choices
  • Ties: 5 choices
  • Jackets: 3 choices
Step 2: Calculate the Total Number of Outfits

To find the total number of different outfits Juan can wear, multiply the number of choices for each item: \[ \text{Total Outfits} = 6 \times 3 \times 5 \times 3 \]

Step 3: Perform the Multiplication

Calculate the product: \[ 6 \times 3 = 18 \] \[ 18 \times 5 = 90 \] \[ 90 \times 3 = 270 \]

Final Answer

The total number of different outfits Juan can wear is \(\boxed{270}\).

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