How many possible numbers are between 1 and 1000000000 that are greater than 72000 if we can only use the following digits (4, 5, 6, 7, 8)
To find the number of possible numbers between 1 and 1000000000 that are greater than 72000, and can only use the digits 4, 5, 6, 7, and 8, we can break it down into a step-by-step process:
Step 1: Determine the number of digits in each possible number.
Since each digit must be chosen from the set {4, 5, 6, 7, 8}, we need to figure out the number of digits in each possible number. To do this, we can compare the smallest and largest values in this set with the smallest and largest number possible to form.
The smallest possible number in this set is 4, and the largest possible number is 8. The smallest number we can form is 72001, and the largest number is 8888888888. By comparing these values, we can see that the possible number will have 8 digits.
Step 2: Determine the options for each digit.
Since each digit can only be chosen from the set {4, 5, 6, 7, 8}, there are 5 options for each digit in the possible number.
Step 3: Calculate the total number of possibilities.
To calculate the total number of possibilities, we need to find the number of ways to arrange the options for each digit. Since there are 8 digits in the possible number and 5 options for each digit, we can calculate it as 5^8, which is equivalent to multiplying 5 by itself 8 times.
Using a calculator, we can find that 5^8 is equal to 390,625. Therefore, there are 390,625 possible numbers between 1 and 1000000000 that are greater than 72000 and can only use the digits 4, 5, 6, 7, and 8.