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  4. A seven-digit number made up of all distinct digits 8, 7, 6, 4, 2, x and y is divisible by 3 then possible number of order pair (x, y) is

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Q. A seven-digit number made up of all distinct digits $8, 7, 6, 4, 2, x$ and $y$ is divisible by 3 then possible number of order pair $(x, y) $ is

Permutations and Combinations

Solution:

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Sum of digits $=8+7+6+4+2+x+y=27+x+y$
For divisible by 3 , sum must be divisible by 3
$\therefore$ pairs of $x$ and $y$ is $(0,3),(0,9),(3,0),(9,0),(1,5),(3,9),(5,1),(9,3)$ out of $0,1,3,5,9$
Number of order pair $(x, y)$ is $8 .$