There are $$4$$ purple, $$4$$ white and $$4$$ red balls in a bag. Without looking into the bag, at least how many balls must be drawn so that there will definitely be $$3$$ \uline{different} coloured balls? 
Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations