Hint : Expand.! :P

Discrete Mathematics Level pending

If \(^{ n }{ C }_{ r }+3^{ n }{ C }_{ r-1 }+3^{ n }{ C }_{ r-2 }+^{ n }{ C }_{ r-3 }=^{ n+k }{ C }_{ r }\) for every \(n,r\epsilon N\) \(r\epsilon [3,n+3]\). Find \({ k }^{ 4 }-1\).

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