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What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6,

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GMAT 1: 700 Q50 V34
Re: What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, [#permalink]

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New post 11 Mar 2018, 04:06
Set = {1,2,3,4,5,6,7,8,9}
Modulo by 3 = {1,2,0,1,2,0,1,2,0}

so if we remove {0,0} or {1,2} combos from the set, remaining set sum will be divisible by 3

selecting {0,0}, there are three numbers with modulo 0, => 3c2 = 3
selecting {1,2}, there are three numbers with modulo 1 and three numbers with modulo 2, 3C1 * 3C1 = 9

total {0,0} + {1,2} = 12
Re: What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6,   [#permalink] 11 Mar 2018, 04:06
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What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6,

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