2004 AMC 10B Problems/Problem 2
Contents
Problem
How many two-digit positive integers have at least one as a digit?
Solution 1
Ten numbers have as the tens digit. Nine numbers have it as the ones digit. Number is in both sets.
Thus the result is .
Solution 2
We use complementary counting. The complement of having at least one as a digit is having no s as a digit.
We have digits to choose from for the first digit and digits for the second. This gives a total of two-digit numbers.
But since we cannot have as a digit, we have first digits and second digits to choose from.
Thus there are two-digit numbers without a as a digit.
(The total number of two-digit numbers) (The number of two-digit numbers without a ) .
See also
2004 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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