To determine how many different outfits Juan can wear if he chooses one tie, one shirt, and one pair of pants for each outfit, we need to consider all of the possible combinations he can make with the items he has.
1. Ties: Juan has 3 ties.
2. Shirts: Juan has 5 shirts.
3. Pants: Juan has 5 pairs of pants.
When calculating the total number of different outfits, we should multiply the number of choices for each article of clothing together. Specifically, the total number of different outfits Juan can wear is found using the formula:
[tex]\[ \text{Number of different outfits} = (\text{Number of ties}) \times (\text{Number of shirts}) \times (\text{Number of pants}) \][/tex]
Plugging in the numbers we have:
[tex]\[ \text{Number of different outfits} = 3 \times 5 \times 5 \][/tex]
Thus, the number of different outfits Juan can wear is:
[tex]\[ 75 \][/tex]
Therefore, there are 75 different outfits Juan can wear if he chooses one tie, one shirt, and one pair of pants for each outfit.
