In how many ways can a person order one ice cream cone with three different flavors of ice cream if there are 15 flavors to choose from and it matters to the person how the 3 flavors are stacked on the one come? That is,which flavor is on the top,middle,and bottom.
To find the number of ways a person can order one ice cream cone with three different flavors, we can use the concept of permutation.
Since there are 15 flavors to choose from and the order matters, we need to find the number of permutations of 15 items taken 3 at a time. This can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
In this case, n = 15 (the number of flavors) and r = 3 (the number of flavors on the cone).
P(15, 3) = 15! / (15 - 3)!
= 15! / 12!
= 15 × 14 × 13
= 2730
Therefore, there are 2,730 ways a person can order one ice cream cone with three different flavors of ice cream.