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Total number of ways of selecting two nu...

Total number of ways of selecting two numbers from the set `{1, 2, 3, ..., 90}` so that their sum is divisible by 3, is

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Given number can be rerranged as
` 1" " 4" " 7…….88 to 30`
`2" " 5" "8…..89 to 30`
`3" "6" "9 to 30`
That means we must take two numbers from last row or one number each from from first and second law. Total ways `=""^(30)C_(2)+""^(30)C_(1)*""^(30)C_(1)=435+900=1335`
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