How many even numbers greater than 40000 that can be formed from the following digits 1,0,2,4,6,7,8

4, 6,7, 8 in the ten thousands

0,1,2,4,6,7,8 can be used in the thousands
hundreds and tens could use any of the digits

ones would have to be 0,2,4,6,8

if we can repeat the digits then
4 times 7 times 7 times 7 times 5

The only problem is that we don't want to have 40000 snd this could happen with the above. Can you think about what you would have to do to eliminate that possibility?

To find the number of even numbers greater than 40000 that can be formed using the given digits (1, 0, 2, 4, 6, 7, 8), we can break down the problem into several steps:

Step 1: Determine the total number of options for each position.
In this case, the positions we need to consider are the ten-thousands place, thousands place, hundreds place, tens place, and units place.

For the ten-thousands place (the first digit), we cannot use the digit "0," so the number of options is five because we can choose from 1, 2, 4, 6, 7, or 8.

For the remaining positions (thousands place, hundreds place, tens place, and units place), we can use any of the given digits (1, 0, 2, 4, 6, 7, 8). Therefore, the number of options for each of these positions is 7.

Step 2: Multiply the number of options
Since each position is independent, we can find the total number of even numbers by multiplying the number of options at each position.

So, the total number of even numbers greater than 40000 that can be formed is:
5 (options for the ten-thousands place) × 7 (options for each remaining position) × 7 × 7 × 7 = 5 × 7^4 = 5 × 2401 = 12,005

Therefore, there are 12,005 even numbers greater than 40000 that can be formed using the given digits.