Mock AIME 3 Pre 2005 Problems/Problem 2
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 |