Problem:
The members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let be the number of different assignments of flavors to players that meet these conditions. Find the remainder when is divided by .
Solution:
The total number of valid assignments is
so the remainder when is divided by is .
The problems on this page are the property of the MAA's American Mathematics Competitions