What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?	Select the correct option.
A) 10  B) 11  C) 12  D) 13  E) 14
We describe 2 solutions. Let S = {1, 2, . . . , 9}. Observe that the sum of the elements of S   is divisible by 3. So the problem is the same as asking for the number of ways that 2 elements   of S can be chosen so that their sum is divisible by 3 (the other 7 elements of S correspond to a   7-element set as in the problem). Choosing 2 elements of S with sum divisible by 3 corresponds   to either choosing 2 numbers divisible by 3 (which can be done in 3 ways) or choosing 1 number   that is one more than a multiple of 3 and 1 number that is one less than a multiple of 3 (which can   be done in 3 · 3 = 9 ways). Hence, the answer is 3 + 9= 
<gadget id="calculator">3 + 9</gadget>
<output>12</output>
12.   correct answer 12
<result>C</result>
What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?