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## Homework Statement

Roll a fair die three times

Let X be the number of different faces shown all together ( X = 1,2,3 )

Find px(k)

## Homework Equations

## The Attempt at a Solution

Alright so I kno that i need to get the individual probabilities of each outcome

The first one where only one face is shown is (1/6)^3 * 6

The one where there are two different faces is (1/6)^2 * (5/6)

And I assume that likewise the final one with three different ones is (1*5*6)/(6^3)

Where Im getting stuck is I kno they have to sum to one so finding the different combinations to multiply to these expressions is giving me some trouble. For example the combinations in the same face was 6 becuase it could be either 1,2,3,4,5,6. Currently I have part 2 as having 30 different outcomes but it winds up looking a little off...any help would be great