Given **six distinct colors**, in how many **unique** ways can a **six faced cube** be painted such that no two faces have the same color?

*Note: Mixing of colors is not allowed.*

**Answer: **30 ways

**Explanation: **

To avoid repetitions, let us fix the color of the top face.

Hence, the bottom face can be painted in **5 ways**.

Now, what remains is the circular arrangement of the remaining four colors which can be done in **(4-1)!** = **3!** = **6 ways** (For **n** distinct objects, number of distinct circular arrangements are **(n-1)!**).

Hence, the answer is **5*6** = **30 ways**.