Given that S = {1,2,3,.....,14}, determine the total number of 7-element subsets of S such that the sum of elements of each of the subsets is divisible by 14
I believe the answer is 1+21+35+7= 64.
1 for the basic set of 1,2,3...7 - sums up to 28.
COMB(7,2)=21 for sets formed by augmenting any 2 of the 7 numbers by 7, like 8,9,3,4,5,6,7
COMB(7,4)=35 for sets formed by augmenting any 4 of the 7 numbers by 7, like 8,9,10,11,5,6,7
COMB(7,6)=7 for sets formed by augmenting any 6 of the 7 numbers by 7, like 8,9,10,11,12,13,7
0,2,4 or 6 members of (1,2,3,4,5,6,7) needed to be changed- half of the sum of the 7th line in Pascal triangle, i.e. 2^6=64
Edited on June 29, 2015, 4:38 pm
simple count
