Question

20 points! A home alarm system randomly assigns a four-character code for each person. The code will not repeat a character. The characters are 2, 3, 4, 5, M, V, T, or R. What is the total number of codes that can be randomly assigned?

Answer 1

There are 8 items in the set {2, 3, 4, 5, M, V, T, R}

We have 8 choices for the first slot
After making that choice,we have 7 left over (since we can't repeat a digit)
Then after that we have 6 choices
Finally there are 5 choices for slot 4

Multiply out these values: 8*7*6*5 = 1680

Answer: 1680

Side Note:
You can use the nPr formula to get the same result.
You would use n = 8 and r = 4
The nPr formula is 
nPr = (n!)/(n-r)!