A set of four distinct numbers are chosen from the set {1,2,3…9,10,11}. How many ways can this set of 4 numbers be chosen such that the sum is divisible by 3?

Choosing the numbers {1,2,3,6} is the same as choosing the numbers {6,3,2,1}.

Question

A set of four distinct numbers are chosen from the set {1,2,3…9,10,11}. How many ways can this set of 4 numbers be chosen such that the sum is divisible by 3?

Choosing the numbers {1,2,3,6} is the same as choosing the numbers {6,3,2,1}.

anonymous · Answer

hint::

leaving remainder 0 are 3,6,9
leaving remainder 1 are 1,4,7,10
leaving remainder 2 are 2,5,8,11