2002 AMC 10P Problems/Problem 3
Contents
[hide]Problem
Mary typed a six-digit number, but the two s she typed didn't show. What appeared was How many different six-digit numbers could she have typed?
Solution 1
This is equivalent to since we are choosing spots (three in between and two to the left and right with two s. We also have to take into account "double s," namely, and in our spots.
Thus, our answer is
Solution 2
We can split this into a little bit of casework which is easy to do in our head.
Case 1: The first is ahead of the first Then the second has places.
Case 2: The first is below the first Then the second has places.
This continues as the answer comes to
Thus, our answer is
Solution 3
We can just count the cases directly since there are so little.
Thus, our answer is
See also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AMC 10 Problems and Solutions |
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