2011 AMC 10A Problems/Problem 13
Problem 13
How many even integers are there between and whose digits are all different and come from the set $\left\{1,2,5,7,8,9}\right$?$ (Error compiling LaTeX. ! Extra }, or forgotten \right.)\text{(A)}\,12 \qquad\text{(B)}\,20 \qquad\text{(C)}\,72 \qquad\text{(D)}\,120 \qquad\text{(E)}\,200$
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 possibilities.
See Also
2011 AMC 10A (Problems • Answer Key • Resources) | ||
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Followed by Problem 14 | |
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