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In the expansion of ( 1 + x+ x^(2) + x^(...

In the expansion of `( 1 + x+ x^(2) + x^(3))^(6)` , the coefficient of `x^(14)` is `:`

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`( 1+ x + x^(2) +x^(3))^(6) = ( 1+ x )^(6) `
`= ( ""^(6) C_(0) + ""^(6) C_(1) x + ""^(6) C_(2) x^(2) + ""^(6) C_(3)x^(3) + ""^(6) C_(4) x^(4) + ""^(6) C_(5) x^(5) + ""^(6) C_(6) x^(6))xx ( ""^(6) C_(0) + ""^(6) C_(1) x^(2) +""^(6) C_(2) x^(4)+""^(6) C_(4) x^(8)+ ""^(6) C_(5) x^(10) + ""^(6) C_(6) x^(12) ) `
`:. ` Coefficient of `x^(14)` in `( 1+ x+ x^(2) + x^(3))^(6)`
`= ""^(6) C_(2). ""^(6) C_(6) + ""^(6) C_(4).""^(6) C_(5)+ ""^(6) C_(6).""^(6)C_(4) = 15+ 90 + 15 = 120`
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