Weekly Problem 21 - 2013

Stage: 1 Challenge Level: Challenge Level:1

In how many different ways can seven different numbers be chosen from the numbers $1$ to $9$ inclusive so that the seven numbers have a total which is a multiple of $3$?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
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