How many five-digit even numbers, that are less than 50000 and that are not divisible by 5, can be created from the digits 0, 1, 3, 5, 6, 7, 8 and 9, if no digit can be used more than once?

To find the number of five-digit even numbers less than 50,000 and not divisible by 5, using the digits 0, 1, 3, 5, 6, 7, 8, 9 without repetition, we follow these steps:

Step 1: The first digit Since the number must be less than 50,000, the first digit can only be 1, 3, or 4. However, 4 is not in our list of digits, leaving us with only two possibilities: 1 or 3.

Step 2: The last digit The last digit must be even and not 0 (since the number cannot be divisible by 5). Our even digit options are 0, 6, and 8. Since 0 is not allowed (we do not want a number divisible by 5), we have two valid options for the last digit: 6 or 8.

Step 3: Digits in between For the three digits in the middle, we can use any of the remaining six digits that haven't been used for the first and last places, which gives us 6 choices for the second position, 5 choices for the third position, and 4 choices for the fourth position.

Step 4: Putting it all together We now multiply the number of choices for each position. There are 2 choices for the first digit, 6 choices for the second, 5 for the third, 4 for the fourth, and 2 for the fifth (last digit).

So the total number of possible numbers is 2 (first digit) * 6 (second digit) * 5 (third digit) * 4 (fourth digit) * 2 (fifth digit).

2 * 6 * 5 * 4 * 2 = 480

There are 480 different five-digit even numbers less than 50,000 that are not divisible by 5 and can be created from the digits given without repeating any digit.