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.
 A: Your answer for the first part looks good.
For the second question, I would divide the answer into two terms, one for black and yellow shirts, and one for the other colored shirts:
$$2\cdot 5 + 4\cdot 5\cdot 2\cdot 2.$$
The first term is for the black and yellow shirts. They only come in short sleeve and solid, so the only variation of these two colors are the five different sizes, hence $2\cdot 5$. The second term is just all the combinations for the four remaining colors.
A: 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 $10 + 80 = 90$.
A: This is another way in which you can get your answer from 1 part
Total cases for 6 colours=120. Since all cases are equally distributed each colour has 20 types of shirts so combining yellow and black there are 40 shirts. In part 2 the no of cases for black and yellow are reduced by a factor of 4 so finally total black and yellow shirts are 10 ans =120-(40-10)
