Order of ingredients question Chocolate milk is made of 5 ingredients. We put those ingredients one after another in a way that only the sugar or the cocoa can be the first ingredient entered and we have to pour the milk after the water (not directly after, just after). The fifth ingredient is not important, lets call it Vanilla. In how many ways can you make chocolate milk ? I'm just not sure if we need to use the inclusion exclusion method because maybe I'm counting things twice. Thanks in advance !

We have two choices for the first ingredient, which leaves us with four choices for the second ingredient, three choices for the third ingredient, two choices for the fourth ingredient, and one choice for the fifth ingredient. However, in half these choices, we added the milk before we added the water. Thus, the number of ways of making chocolate milk is $$\frac{1}{2} \cdot 2 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 24$$