Question

how many 3-letter \words\ (including nonsense words) can be formed using the 5 letters a, b, c, d, and e if each letter is used at most once?

$_{5}\mathrm{p}_{3} = ?$

Explanation:

Step1: Recall permutation formula

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

Step2: Calculate factorial values

$5! = 5×4×3×2×1 = 120$, $(5-3)! = 2! = 2×1 = 2$.

Step3: Compute the result

$P(5,3)=\frac{120}{2}=60$.

Answer:

60