You make a map of all 64 possible outcomes for this 3-candy package. It turns out that for 36 of the outcomes, any two candies will match. Given what you already know about packages with all three having the same color, how many out of the 64 possibilities will involve all three candies being DIFFERENT colors?

24

Step-by-step explanation:

We have a package with 3 candy, so we have N = 3.

Now, if n is the number of possible colours of the candy, we have that the number of outcomes can be written as:

C = n^N = n^3

and we know that C = 64

64 = n^3

n = ∛64 = 4.

So we have 4 possible colours.

Now, we want the combinations where all 3 candies have different colors, then:

For the first candy, the options for colours are 4.

For the second candy, the options for colours are 3 (because 1 is already taken)

for the last candy, the options for colours are 2 (because 2 are already taken)

then the number of combinations is c = 4*3*2 = 24