Use the Permutations Formula
-How many 2-letter codes can be formed using the letters A, B, C, D, E, and F? No letter can be used more than once.
A) 30
B) 360
C) 15
D) 720

Question

Quizplus · Accepted Answer

The number of 2-letter codes that can be formed from 6 letters without repetition is calculated using the permutation formula P(n, r) = 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 factorial of the difference between n and r. Here, n=6 (letters A, B, C, D, E, F) and r=2 (because we are forming 2-letter codes), so P(6, 2) = 6! / (6-2)! = 6! / 4! = (6×5×4!)/4! = 30.