Let S={1,2,3,5,7,10,11}. The number of nonemp | vedclass

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Question

Elements of the type $3 k =3$

Elements of the type $3 k +1=1,7,9$

Elements of the type $3 k +2=2,5,11$

Subsets containing one element $S_1=1$

Vedclass · Accepted Answer

$43$

Vedclass · Answer

Elements of the type $3 k =3$

Elements of the type $3 k +1=1,7,9$

Elements of the type $3 k +2=2,5,11$

Subsets containing one element $S_1=1$

Subsets containing two elements

$S_2={ }^3 C_1 	imes{ }^3 C_1=9$

Subsets containing three elements

$S_3={ }^3 C_1 	imes{ }^3 C_1+1+1=11$

Subsets containing four elements

$S_4={ }^3 C_3+{ }^3 C_3+{ }^3 C_2 	imes{ }^3 C_2=11$

Subsets containing five elements

$S_5={ }^3 C_2 	imes{ }^3 C_2 	imes 1=9$

Subsets containing six elements $S_6=1$

Subsets containing seven elements $S_7=1$

$\Rightarrow 	ext { sum }=43$

Let $S=\{1,2,3,5,7,10,11\}$. The number of nonempty subsets of $S$ that have the sum of all elements a multiple of $3$ , is $........$

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