Five digit numbers are made using the numbers 0 to 7

3,720 ways

Step-by-step explanation

Given: numbers 0 to 7 = 0, 1, 2, 3, 4, 5, 6, 7 = total of 8 numbers

Even numbers are 0, 2, 4, 6

Any 5-digit number that has the last digit of 0, 2, 4 and 6 are made of even numbers, as it is divisible by 2.

First, we choose 0 for the last digit.  

That's 1 way. Choose the first digit 7 ways (excluding 0).

Choose the 2nd digit 6 ways.   

 Choose the 3rd digit 5 ways.    

Choose the 4th digit 4 ways.

That's 7 * 6 * 5 * 4 * 1 = 840 ways

Second, we choose 2,4 or 6 being the last digit.

That's 3 ways. Choose the first digit 6 ways (0 can't be a first digit).

Choose the 2nd digit 6 ways.   

 Choose the 3rd digit 5 ways.    

Choose the 4th digit 4 ways.

That's 6 * 6 * 5 * 4 * 4 = 2,880 ways

Thus, we have the 

total of even numbers that can be made = 840 + 2,880 = 3,720 ways