1993 AIME Problems/Problem 1
Problem
How many even integers between 4000 and 7000 have four different digits?
Solution
The thousands digit is .
Case : Thousands digit is even
, two possibilities, then there are only
possibilities for the units digit. This leaves
possible digits for the hundreds and
for the tens places, yielding a total of
.
Case : Thousands digit is odd
, one possibility, then there are
choices for the units digit, with
digits for the hundreds and
for the tens place. This gives
possibilities.
Together, the solution is .
See also
1993 AIME (Problems • Answer Key • Resources) | ||
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