Using the digits 9, 8, 2, 5 exactly once, how many numbers greater than 5000 can be formed?

Question: Using the digits 9, 8, 2, 5 exactly once, how many numbers greater than 5000 can be formed?

Solution:
To form a number greater than 5000, the first digit must be one of 5, 8, or 9.
If the first digit is 5, the remaining 3 digits can be arranged in ³P₃ = 6 ways.
If the first digit is 8, the remaining 3 digits can be arranged in ³P₃ = 6 ways.
If the first digit is 9, the remaining 3 digits can be arranged in ³P₃ = 6 ways.

Therefore, the total number of ways to form such numbers is: 6 + 6 + 6 = 18
18 numbers greater than 5000 can be formed.