Question

How many arrangements of the letters in the word o l i v e can you make if each arrangement must use three letters?

A. 60
B. 5 · 4 · 3 · 2 · 1
C. 20
D. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1

Answer 1

Since they are all unique letters, we don't need to worry about overcounting factors.
Now, we want arrangements, so the order does matter. The arrangement: OLI is not the same as ILO, since they are counted as different words.

Thus, using the permutation formula, we get:
$^{5}P_3 = \frac{5!}{(5 - 3)!} = \frac{5!}{2!} = 5 \cdot 4 \cdot 3 = 60$

So, the answer is (A) 60