how many ways can 3 letter permutations be formed from the first 5 letters of the alphabet?

Explanation:

Step1: Recall permutation formula

The permutation formula is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen. Here $n = 5$ (the first 5 letters of the alphabet) and $r=3$.

Step2: Calculate factorial values

$n!=5!=5\times4\times3\times2\times1 = 120$ and $(n - r)!=(5 - 3)!=2!=2\times1=2$.

Step3: Substitute into formula

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

Answer:

60