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To determine how many different sets Jean can compose using one of each garment category, you multiply the number of choices available in each category together.

Jean has the following options:

- 5 shirts

- 3 ties

- 6 trousers

- 2 coats

To find the total number of combinations, you calculate:

5 (shirts) × 3 (ties) × 6 (trousers) × 2 (coats)

Carrying out this multiplication step-by-step:

- First, multiply the number of shirts and ties:

5 × 3 = 15

- Next, multiply this result by the number of trousers:

15 × 6 = 90

- Finally, multiply by the number of coats:

90 × 2 = 180

Thus, the total number of different sets Jean can compose is 180. This total takes into account every combination of one item from each clothing category, demonstrating how selection across multiple categories leads to a comprehensive number of outfit possibilities.

The other choices represent either underestimations or overestimations of these combinations, as they do not account for the actual counts in each category and the multiplication of those counts.