Question

All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by six numbers. How many possible different ID numbers are there?

(a) 26,000,000
(b) 456,976,000
(c) 10,000,000
(d) 1,679,616

Answer 1

To determine the number of possible ID numbers at ABC Company, we multiply the number of options for the letter (26) by the possible combinations for the six digits (10^6), resulting in 26,000,000 different IDs.

Step-by-step explanation:

To calculate the number of possible different ID numbers for employees at ABC Company, we need to take into account that each ID consists of a letter followed by six numbers. There are 26 letters in the alphabet, so there are 26 possible choices for the first character. After the letter, there are six digits, and each digit can be any number between 0 to 9, which gives us 10 possibilities for each of the six positions.

The total number of different ID numbers can be found by multiplying the number of choices for each position in the ID. For the letter, we have 26 possibilities, and for each digit in the six-digit number, we have 10 possibilities. Therefore, the calculation would be 26 (letters) multiplied by 10^6 (for the six numbers), which is:

26 * 10^6 = 26,000,000

So, the correct answer is (a) 26,000,000.