Linda picks $3$ different numbers from $$1-15$$. To make the sum of the three numbers divisible by $3$, how many different groups are there for Linda to pick? 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations
Group $A$: $$1$$, $$4$$, $$7$$, $$10$$, $13$;  Group $B$: $$2$$, $$5$$, $$8$$, $$11$$, $$14$$;  Group $C$: $$3$$, $$6$$, $$9$$, $$12$$, $$15$$.  Linda can choose three numbers from the same group, or choose each number from a different group to get the sum she needs.  There are $3\times\_5C\_3+5\times5\times5=155$ groups. 