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Question

Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that a2b2  is divisible by 3



Solution

The correct option is D


G1:3,6,9......3nG2:1,4,7.....(3n2)G3:2,5,8....(3n1)a2b2=(ab)(a+b)
Either a-b is divisible by 3 (or) a + b is divisible by 3 (or) both
nc2+nc2+nc2+nc1.nc13n(n1)2+n2
 

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