2006 Alabama ARML TST Problems/Problem 4
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Problem
Find the number of six-digit positive integers for which the digits are in increasing order.
Solution
We pick six different digits 
through 
for the integer. None of them can be 0, or else it is a five digit integer or the digits are not in increasing order. Let's say that is the least digit of them all. is therefore the hundred-thousands digit. Let's say that 
is the second smallest integer. Then is the ten-thousands digit. etc.
For each group of 
we pick, there is only one arrangement such that each digit is in increasing order. There are 
ways to pick the digits, therefore there are 84 integers.
See also
| 2006 Alabama ARML TST (Problems) | ||
| Preceded by: Problem 3 | Followed by: Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
