Elementary Combinatorics... How many different shirts are being sold? A shirt sold in 6 colors, 5 sizes, striped or solid, and long sleeve or short sleeve. -How many different shirts are being sold? -What if the black and yellow shirts only come in short-sleeve and solid? For the first part, it seems that the answer is simply $6 \cdot 5 \cdot 2 \cdot 2 = 120$ different shirts. However, the second part is throwing me off.

Your answer to the first question is correct.

If the shirt is black or yellow, there are five sizes, one choice for striped or solid (namely solid), and one choice for long sleeve or short sleeve (namely short sleeve). Hence, there are $2 \cdot 5 \cdot 1 \cdot 1 = 10$ shirts that are black or yellow.

For the other four colors, we have five sizes, the choice of striped or solid, and the choice of long or short sleeve, so there are $4 \cdot 5 \cdot 2 \cdot 2 = 80$ shirts that are neither black nor yellow.

Hence, the number of different shirts in the second question is $10 + 80 = 90$.