An ice cream shop has 19 flavors. You also have the choice of a sugar cone, waffle cone or cup. If a person orders two scoops of different flavor ice cream, how many possible orders are there, if you do not care about the order of flavors?
I don't understand how to factor in the two different flavors? I solved for P(19,3) and I think it is wrong because I need the two scoops possibility
Well, if you don't care about the order of flavors, then you can think of it this way: for each scoop, you have 19 options to choose from. Since you want to order two scoops of different flavor ice cream, you can choose the first scoop in 19 different ways, and then choose the second scoop in 18 different ways (since you've already picked one flavor).
To find the total number of possible orders, you can multiply these two numbers together: 19 * 18 = 342.
So, there are 342 possible orders if you want two scoops of different flavors.
To determine the number of possible orders when choosing two scoops of different flavor ice cream, you need to use the concept of combinations.
First, consider the number of choices you have for the first scoop. You can choose any of the 19 flavors.
Next, for the second scoop, you need to consider that you cannot choose the same flavor as the first scoop since you want different flavors. So, for the second scoop, you have 18 remaining flavors to choose from.
To calculate the total number of possible orders, you need to multiply the number of choices for the first scoop by the number of choices for the second scoop. Therefore, the number of possible orders is 19 * 18 = 342.
In this case, using combinations (such as P(19, 3)) is not appropriate because combinations consider the order or arrangement of elements, while in this problem, the order of the two flavors does not matter.
Hence, the correct solution is to multiply the number of choices for each scoop, as explained above, giving a total of 342 possible orders.
first scoop has 19 choices
second has 18 choices
cone has 3 choices
18*19*3
First scoop have 18*3 choice
Second scoop have 18*3-1 choice..
So total 108*107