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in Permutations and combinations by (52.7k points)

The smallest possible value of S = a1.a2.a3 + b1.b2.b3 + c1 . c2.c3, where a1,a2,a3,,b1,b2,b3,c1,c2,c3 is a permutation of the number 1, 2, 3, 4, 5, 6, 7, 8, and 9 is

(A)  213

(B)  216

(C)  324 

(D)  214

1 Answer

+1 vote
by (46.6k points)
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Best answer

Correct option (D) 214

The idea is to get 3 terms as close as possible.

We have 214 = 70 + 72 + 72

= 2⋅5⋅7 + 1⋅8⋅9 + 3⋅4⋅6 by AM ≥ GM

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