Solve the problem.
-A college identification number consists of a letter followed by 4 digits. How many different identification numbers are possible if repetition is not permitted?
A)144
B)468,000
C)5690
D)3,276,000

Question

Quizplus · Accepted Answer

There are 26 choices for the initial letter, and since repetition is not permitted, there are 10 choices for each of the 4 digits (since there are 10 possible digits). Therefore, the total number of possible identification numbers is:

26 × 10 × 9 × 8 × 7 = 3,276,000

So, the answer is D. There are 26 letters in the alphabet and 10 digits (0-9). 
Therefore, the number of possible identification numbers is:
26 options for the first letter x 10 options for the second digit x 9 options for the third digit x 8 options for the fourth digit 
= 26 x 10 x 9 x 8  
= 20,160 
However, the problem states that repetition is not permitted, so we must use the permutation formula:
nPr = n! / (n-r)!
Where n is the number of options and r is the number of selections. 
In this case, we have 26 options for the first letter (n=26) and we are selecting one (r=1). We have 10 options for the second digit (n=10) and we are selecting one (r=1), and so on. 
Using the permutation formula, we get:
26P1 x 10P1 x 9P1 x 8P1 
= 26 x 10 x 9 x 8 
= 18,720 
Therefore, the correct answer is D) 3,276,000.

Solve the Problem. -A College Identification Number Consists of a Letter Followed by Letter