Difference between revisions of "2011 AMC 10A Problems/Problem 13"
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==Problem 13== | ==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}? | + | How many even integers are there between <math>200</math> and <math>700</math> whose digits are all different and come from the set <math>{1,2,5,7,8,9}</math>? |
<math>\text{(A)}\,12 \qquad\text{(B)}\,20 \qquad\text{(C)}\,72 \qquad\text{(D)}\,120 \qquad\text{(E)}\,200</math> | <math>\text{(A)}\,12 \qquad\text{(B)}\,20 \qquad\text{(C)}\,72 \qquad\text{(D)}\,120 \qquad\text{(E)}\,200</math> |
Revision as of 22:25, 25 August 2019
Problem 13
How many even integers are there between and whose digits are all different and come from the set ?
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) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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