how many even 4 digit whole numbers exisit such that the thousands digit it odd all 4 digits different

To find the number of even 4-digit whole numbers where the thousands digit is odd and all four digits are different, we can break down the problem into steps.

Step 1: Determine the number of choices for the thousands digit.
Since the thousands digit should be odd, we have five choices: 1, 3, 5, 7, or 9.

Step 2: Determine the number of choices for the hundreds digit.
Since all four digits must be different, and we have used one of the odd digits for the thousands digit, we have nine remaining options for the hundreds digit.

Step 3: Determine the number of choices for the tens digit.
Again, we must exclude the digit used for thousands and hundreds, so we have eight remaining options for the tens digit.

Step 4: Determine the number of choices for the units digit.
Since we have already used three different digits, we have seven remaining options for the units digit.

Step 5: Calculate the total number of even 4-digit whole numbers that meet the given criteria.
Multiply the number of choices for each digit together:
5 choices for the thousands digit × 9 choices for the hundreds digit × 8 choices for the tens digit × 7 choices for the units digit = 2,520.

Therefore, there are 2,520 even 4-digit whole numbers where the thousands digit is odd and all four digits are different.

To find the number of even 4-digit whole numbers with an odd thousands digit and all four digits different, we can break down the problem into steps:

Step 1: Determine the possible choices for the thousands digit.
Since the thousands digit must be odd, we have five possible choices: 1, 3, 5, 7, or 9.

Step 2: Determine the possible choices for the hundreds digit.
Since all four digits must be different and the thousands digit is odd, we have nine possible choices (0, 2, 4, 6, 8, 1, 3, 5, or 7).

Step 3: Determine the possible choices for the tens digit.
Since all four digits must be different, the thousands digit is odd, and the hundreds digit has been chosen, we have eight possible choices left.

Step 4: Determine the possible choices for the units digit.
Since all four digits must be different, the thousands digit is odd, the hundreds digit has been chosen, and the tens digit has been chosen, we have seven possible choices left.

Step 5: Find the total number of even 4-digit numbers that satisfy the given condition.
Multiplying the number of choices for each digit together, we have:
5 choices for the thousands digit × 9 choices for the hundreds digit × 8 choices for the tens digit × 7 choices for the units digit = 2,520 even 4-digit whole numbers.

Therefore, there are 2,520 even 4-digit whole numbers such that the thousands digit is odd and all four digits are different.