Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 2"
m |
(Tag: Undo) |
| (One intermediate revision by the same user not shown) | |
(No difference)
| |
Latest revision as of 09:16, 29 November 2019
Problem
Let 
denote the number of 
digit positive integers have the property that their digits are in increasing order. Determine the remainder obtained when is divided by 
. (Repeated digits are allowed.)
Solution
Note that a digit increasing integer is determined once we select a set of digits. To determine the number of sets of digits, consider 
urns labeled 
(note that 
is not a permissible digit); then we wish to drop balls into these urns. Using the ball-and-urn argument, having urns is equivalent to 
dividers, and there are 
.
See Also
| Mock AIME 3 Pre 2005 (Problems, Source) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
