Solve the problem.
-How many different 7-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?
A) 4,782,969
B) 36
C) 7
D) 181,440

Question

Quizplus · Accepted Answer

Since there are 9 letters to choose from and no letter can be used more than once, the number of different 7-letter codes can be calculated using permutations. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items to choose from, r is the number of items to choose, n! represents the factorial of n, and (n-r)! is the factorial of the difference between n and r. Here, n = 9 (letters A through I) and r = 7 (the length of the code). Therefore, the calculation is 9P7 = 9! / (9-7)! = 9! / 2! = 362,880 / 2 = 181,440.

Solve the Problem. -How Many Different 7-Letter Codes Are There If Only the If