The question is open to interpretation.
Personally I think that when it says the letters can be arranged in any order it means that they can be arranged in any order and each one of those orders counts as a different combination.
So lets see if I can get an answer given my interpretation.
A certain cryptocode must contain one letter from the set {X, K, M, Z} and three distinct letters from the set {W, X, Y, Z}. The four letters can be arranged in any order, and since X and Z are in both sets, these letters may each appear twice in an arrangement. How many cryptocodes are possible?
| no of combinations | no of permutations each | Total permutations | |
X | X plus 2 of 3 | 3 | 4!/2!=12 | 3*12=36 |
X | No X | 1 | 4!=24 | 1*24=24 |
Y | includes Y | 3 | 12 | 3*12=36 |
Y | No Y | 1 | 24 | 1*24=24 |
Not X or y | Any 3 | 2*4=8 | 4!=24 | 8*24=192 |
Total | 312 |
If my interpretation is correct I get 312 possible crypocodes.