A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5?

Question

Anthony Amato · Accepted Answer

#48 # serial numbers

Consider the number of options for each position. First digit: not 0, not 5. there are 8 options.#" "8xx# Second digit: not 5. not the first digit. 8 options#" "8xx# Third digit: not 5,not 1st or 2nd: 7 options.#" "7xx# Fourth digit: 5. 1 option #" "1xx# Number of unique numbers = #8xx8xx7 = 448#

Andrew Adams · Answer

undefined The total number of four-digit serial numbers that can be created with the digits 0 through 9, where 0 cannot be the first digit, no digit may be repeated, and the last digit must be 5, can be calculated as follows:

- For the first digit: Since 0 cannot be the first digit, there are 9 choices (1 through 9).
- For the second digit: Since no digit may be repeated, there are 9 choices remaining (excluding the digit chosen for the first position).
- For the third digit: There are 8 choices remaining (excluding the digits chosen for the first and second positions).
- For the fourth digit: Since the last digit must be 5, there is only 1 choice.

To find the total number of serial numbers, we multiply the number of choices for each position:

$$ 9 \times 9 \times 8 \times 1 = 648 $$

Therefore, there are 648 four-digit serial numbers that satisfy the given conditions.