Final answer:
To find numbers greater than 7,000 using the digits 1, 3, 7, 8, and 9 without repeats, there are 3 choices for the first digit, then 4, 3, and 2 choices for subsequent digits, leading to a total of 72 possible numbers.
Step-by-step explanation:
To determine how many numbers greater than 7,000 can be formed from the digits 1, 3, 7, 8, and 9 without repetition, we need to consider the place values of a four-digit number. For a number to be greater than 7,000, the first digit (which denotes the thousands place) must be either 7, 8, or 9. Once the first digit is chosen, there are 4 remaining digits to choose from for the hundreds place, 3 left for the tens place, and then 2 for the ones place.
Understanding that, we calculate the number of possibilities as follows:
- First digit (thousands place): 3 choices (7, 8, or 9)
- Second digit (hundreds place): 4 remaining choices
- Third digit (tens place): 3 remaining choices
- Fourth digit (ones place): 2 remaining choices
The total number of possible numbers is thus the product of these choices, which is 3 × 4 × 3 × 2, resulting in 72 possible numbers greater than 7,000.