Question 1159034: How many even numbers are there with three digits such that if 5 is one of the digits in a number then 7 is the next digit in that number in the numbers 0,1,2,3,4,5,6,7,8,9?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
We include all 3-digit even numbers that don't contain a 5 at all.
Case 1: the number does not contain a 5 at all.
We choose the first digit 8 ways [from {1,2,3,4,6,7,8,9}]
We choose the second digit 9 ways [from {0,1,2,3,4,6,7,8,9}]
We choose the third digit 5 ways [from {0,2,4,6,8}].
That's 8∙9∙5 = 360 ways
Case 2: the first digit is a 5 and the second digit is a 7.
They are 570, 572, 574, 576, and 578.
Total 360+5 = 365.
[Note: the 2nd digit cannot be 5 because the third digit must be even, and
thus cannot be 7]
Edwin
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