Combinatorics Problem: Finding Number of Subsets in a Set of Four-Digit Numbers

[Government$]

Homework Statement

Let X be a set containing all four digit numbers made up of {1,2,3}, where every number contains every digit at lease once. Number of all subsets is:

The Attempt at a Solution

So firs i have to find number of elements in the set:

3!*3 + 3*12 = 54

Now what they mean by subsets? And did i calculated number of elements correctly?

 

[haruspex]

54 seems too many. Pls explain your calculation.
For the second part, if there are N elements in a set, how many subsets does it have?

 

[Simon Bridge]

It could be they want to know how many possible subsets of X there are.
i.e. any member of X would be a subset of X of size 1. any pair of members would be a subset size 2, etc.
[haruspex beat me :)]