2007 iTest Problems/Problem 33
Problem
How many four-digit integers have the property that their digits, read left to right, are in strictly decreasing order?
Solution
Use casework to count the total possibilities. Note that order of picking numbers does not matter because there is only one way to arrange a set of digits to decreasing order.
- If the number ends in
, then there are
remaining digits to choose from. Picking
results in
possibilities.
- If the number ends in
, then there are
remaining digits to choose from. Picking
results in
possibilities.
- If the number ends in
, then there are
remaining digits to choose from. Picking
results in
possibilities.
- If the number ends in
or
, then there are less than
remaining digits to choose from, so there are no possibilities in that case.
Adding up the cases results in a total of possibilities.
See Also
2007 iTest (Problems, Answer Key) | ||
Preceded by: Problem 32 |
Followed by: Problem 34 | |
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