How many different 5-letter arrangements can be formed from the letters in the name CATHY if each letter is used only once in each arrangement?

There are 5 ways to choose the first letter, 4 ways to pick the second letter, 3 ways to select the third, 2 options for the fourth letter leaving just one way to pick the final letter.

The number of arrangements are thus 5 x 4 x 3 x 2 x 1 = 120