A warranty identification number for a certain product consists of a letter of the alphabet followed by a four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero?
A) 234,000 numbers
B) 230,000 numbers
C) 232,000 numbers
D) 217,000 numbers
E) 260,000 numbers
F) 266,000 numbers

Question

A warranty identification number for a certain product consists of a letter of the alphabet followed by a four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero? ​
A) 234,000 numbers
B) 230,000 numbers
C) 232,000 numbers
D) 217,000 numbers
E) 260,000 numbers
F) 266,000 numbers

Quizplus · Accepted Answer

The first part of the identification number is a letter of the alphabet, so there are 26 possible choices for this part. The second part is a four-digit number where the first digit must be nonzero. Since there are 9 choices for the first digit (1-9), 10 choices for each of the next three digits (0-9), the total number of possibilities for the four-digit number is 9 * 10 * 10 * 10 = 9,000. Therefore, the total number of possible identification numbers is 26 * 9,000 = 234,000.

A Warranty Identification Number for a Certain Product Consists of a Letter