Question

Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.

If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?

84
504
3,024
60,480

Answer 1

504

Explanation: The last digit is fixed as 7, so the first three digits must be 3 distinct choices from the remaining 9 digits (0–9 excluding 7). Order matters, so 9 × 8 × 7 = 504.