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Q.

A 7-digit number made up of all distinct digits 8,7,6,4,2, x and y is divisible by 3 the, possible number of ordered pair (x,y) is ______

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answer is 8.

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Detailed Solution

 

Sum of the digits divisible by 3
i.e 8+7+6+4+2+x+y=27+x+y is divisible by 3 

 Again since all the seven digit numbers is to have distinct digits therefore x and  y must be chosen from 0,1,3,5,9 (excluding 8,7,6,4,2 ) such that x+y is a   multiple of 3possible ordered pairs are
(0,3)(3,0)(1,5)5,1(0,9)(9,0)(3,9)(9,3)

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