How many permutations exist of the letters a, b, c, d taken four at a time?

answers:
24124

The answer is 24 permutations. 

You can solve this by looking at how many ways we can choose the first letter, second letter... and so on, depending on how many you take at a time (in this case, four at a time)
.
(4 possible letters) x (3 possible letters) x (2 possible letters) x (1 remaining letter) = 24

Or in other words 4! (4 factorial).