Let S= 1 ,2 ,3 ,5 ,7 ,10 ,11 . the number of non empty subsets of S that have the sum of all elements a multiple of 3, is _______

Question

Accepted Answer

Correct answer: 43. (43) Elements of the type 3k=3 Elements of the type 3k+1=1, 7, 9 Elements of the type 3k+2=2,5, 11 Subsets containing one element S_1=1 Subsets containing two elements. S_2=^3C_1 ^3C_1=9 Subsets containing three elements. S_3=^3C_3 ^3C_1+1+1=11 Subsets containg four elements S_4=^3C_3+^3C_3+^3C_2 3_2=11 Subsets containing five elements S_3=^3C_2 ^3C_2 1=9 Subsets containing six elements S_6=1 Subsets containing seven elements S_7=1 ⇒ sum = 43

$Let S = 1, 2, 3, 5, 7, 10, 11 . the number of non empty subsets of S that have the sum of all elements a multiple of 3, is _______$

Solution

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