Question

use an appropriate permutations formula to solve. how many arrangements can be made using three of the letters of the word dozen if no letter is to be used more than once? arrangements (type a whole number.)

Explanation:

Step1: Identify total letters and selection size

The word "DOZEN" has 5 distinct letters. We select 3 letters for arrangement.

Step2: Apply permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$, where $n=5$, $k=3$.

Step3: Calculate the value

$P(5,3)=\frac{5!}{(5-3)!}=\frac{5×4×3×2!}{2!}=5×4×3=60$

Answer:

60