SFF wrote:
A 5-digit code consists of one number digit chosen from 1, 2, 3 and four letters chosen from A, B, C, D, E. If the first and last digit must be a letter digit and each digit can appear more than once in a code, how many different codes are possible?
A. 375
B. 625
C. 1,875
D. 3,750
E. 5,625
A. 375
B. 625
C. 1,875
D. 3,750
E. 5,625
Lets determine the number of ways we can produce each digit.
If L denotes a letter digit and N denotes a number digit, the possibilities for the code are L-N-L-L-L, L-L-N-L-L, and L-L-L-N-L. Note that there are an equal number of possible codes for each of these formats, therefore we will find the number of L-N-L-L-L codes and multiply the result by three.
Since the first digit must be a letter, we have 5 options for the first digit. Since the second digit is a number, there are 3 options for the second digit. For the third, fourth, and fifth digits, we have 5 options each. In total, there are 5 x 3 x 5 x 5 x 5 = 1875 L-N-L-L-L codes. Since the total number of codes is three times that, there are 1875 x 3 = 5625 possible codes.
Answer E