How many ways can you arrange the letters in the word prime?

There are 5 letters in the word "prime"

Imagine we had 5 slots to fill. They are empty initially.

Slot 1 has 5 choices to pick from

Once we pick a letter, we have 4 choices left over for slot 2

Slot 3 will have 3 choices

Slot 4 will have 2 choices

Slot 5 will have 1 choice

We have this countdown: 5,4,3,2,1

which multiplies out to 5*4*3*2*1 = 120

There are 120 unique ways to arrange the letters. Order matters. Because order matters, this is a permutation.