2011 AMC 10A Problems/Problem 13
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Problem 13
How many even integers are there between 200 and 700 whose digits are all different and come from the set {1,2,5,7,8,9}?
Solution
We split up into cases of the hundreds digits being or
. If the hundred digits is
, then the units digits must be
in order for the number to be even and then there are
remaining choices (
) for the tens digit, giving
possibilities. Similarly, there are
possibilities for the
case, giving a total of \boxed{12 \ \mathbf{(A)}} possibilities.