How many four-digit odd numbers can be formed with the digits 0-9 if each digit is used only once in each number?

Sure, here is the step by step solution:

Step 1: Identify the conditions The number is a 4-digit odd number. This means the last digit has to be an odd number. The digits 0-9 can be used but only once in each number.

Step 2: Determine the options for each digit For the last digit (units place), we have 5 options: 1, 3, 5, 7, 9. We can't use 0 because it's not an odd number.

For the first digit (thousands place), we have 9 options. We can't use 0 (a number can't start with 0) and we can't use the digit we used for the units place.

For the second digit (hundreds place), we have 8 options left. We can't use the digits we used for the thousands place and the units place.

For the third digit (tens place), we have 7 options left. We can't use the digits we used for the thousands place, the hundreds place, and the units place.

Step 3: Calculate the total number of 4-digit odd numbers The total number of 4-digit odd numbers is the product of the number of options for each digit. So, it's 9 (for the thousands place) * 8 (for the hundreds place) * 7 (for the tens place) * 5 (for the units place) = 2520.

So, there are 2520 four-digit odd numbers that can be formed with the digits 0-9 if each digit is used only once in each number.