How many 4 digit numbers are greater then 7538 can be made using the digits, 0,3,5,7,8,9 without repetition?
To find the number of 4-digit numbers greater than 7538 that can be made using the digits 0, 3, 5, 7, 8, and 9 without repetition, we can break down the problem into smaller steps:
Step 1: Determine the available choices for each digit position.
Since repetition is not allowed, we will have fewer choices for each digit position as we move from left to right.
For the first digit (thousands place), only the digits 7, 8, 9 are available because we want numbers greater than 7538.
For the second digit (hundreds place), any of the remaining digits can be used (0, 3, 5, 7, 8, 9) because repetition is not allowed.
For the third digit (tens place), any of the remaining digits can be used (0, 3, 5, 7, 8, 9) because repetition is not allowed.
For the fourth digit (ones place), any of the remaining digits can be used (0, 3, 5, 7, 8, 9) because repetition is not allowed.
Step 2: Calculate the total number of possible combinations.
Multiply the number of choices for each digit position.
For the first digit (thousands place), we have 3 choices (7, 8, 9).
For the second digit (hundreds place), we have 5 choices (0, 3, 5, 8, 9).
For the third digit (tens place), we have 4 choices (0, 3, 5, 9).
For the fourth digit (ones place), we have 3 choices (0, 5, 9).
Multiply all the choices together: 3 * 5 * 4 * 3 = 180.
Therefore, there are 180 four-digit numbers greater than 7538 that can be made using the digits 0, 3, 5, 7, 8, and 9 without repetition.