Use the Permutations Formula
-How many 3-letter codes can be formed using the letters $A , B , C , D$, and E? No letter can be used more than once.
A) 60
B) 20
C) 10
D) 40

Question

Quizplus · Accepted Answer

The number of 3-letter codes that can be formed from 5 distinct letters without repetition is calculated using the permutations formula $nPr = \frac{n!}{(n-r)!}$, where $n$ is the total number of items to choose from, $r$ is the number of items to choose, $n!$ denotes the factorial of $n$, and $n-r$ is the difference between the total number of items and the number of items chosen. Here, $n = 5$ (letters A, B, C, D, E) and $r = 3$ (since we are forming 3-letter codes). Thus, the calculation is $5P3 = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{120}{2} = 60$.

Use the Permutations Formula -How Many 3-Letter Codes Can Be A,B,C,DA , B , C , DA,B,C,D

Use the Permutations Formula
-How Many 3-Letter Codes Can Be $A , B , C , D$