Randolph has 8 ties, 6 pants, and 4 dress shirts. How many days could he go without wearing the same combination of these three items?

• A. 144 days
• B. 192 days
• C. 128 days
• D. 96 days

Answer: (B)

Counting combinations using the multiplication principle: when you form an outfit, you pick one item from each category and the choices multiply because every tie can be paired with every pant, and that pair can be worn with every shirt.

Randolph has 8 ties, 6 pants, and 4 dress shirts. For each tie, there are 6 pants to choose from, giving 8 × 6 = 48 tie-pant combinations. Each of these can be matched with any of the 4 shirts, so 48 × 4 = 192 distinct outfits.

Therefore, he could go 192 days without repeating the same combination.