Problem
Julio is dressing for an interview. He has a green, a red, a black, a brown, and a blue jacket. He has two pairs of tan slacks, one gray pair, two brown pairs, and one blue pair. His shirts are white, gray, blue, and yellow. He has two red ties, two blue ties, and one brown tie. If he wears the blue jacket, he will not wear anything else that is blue or brown; otherwise, there are no restrictions. (a) How many outfits can he select if he wears the blue jacket? (b) How many outfits can he wear if he does not wear the blue jacket? (c) How many total outfits can he wear? (a) If he wears the blue jacket then he has outfits he can wear. (Type a whole number.)
Solution
Step 1 ：Julio has a choice of 3 pairs of slacks (2 tan and 1 gray), 3 shirts (white, gray, and yellow), and 2 red ties if he wears the blue jacket.
Step 2 ：The total number of outfits he can wear with the blue jacket is calculated by multiplying the number of choices for each item of clothing.
Step 3 ：So, the total number of outfits is \(3 \times 3 \times 2 = 18\)
Step 4 ：Final Answer: The number of outfits Julio can select if he wears the blue jacket is \(\boxed{18}\)
