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The coefficient of x^(-17) in the expans...

The coefficient of `x^(-17)` in the expansion of `(x^4-1/x^3)^(15)` is

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Given expansion is `(x^(4) - (1)/(x^(3)))^(15)`
Let the term `T_(r + 1)` constains the coefficient of `(1)/(x^(17))` i.e., `x^(-17)`
`:. T_(r + 1) = .^(15)C_(r) (x^(4))^(15 - r) (-(1)/(x^(3)))^(r)`
`= .^(15)C_(r) x^(60 - 4xr) (-1)^(r) x^(-3r)`
`.^(15)C_(r) x^(60 - 7r) (-1)^(r)`
For the coefficient `x^(-17)`,
`60 - 7r = - 17`
`rArr 7 r = 77 rArr r = 11`
`rArr T_(11 + 1) = .^(15)C_(11) x^(60 - 77) (-1)^(11)`
`:.` Coefficient of `x^(-17) = (-15 xx 14 xx 13 xx 12 xx 11 !)/(11! xx 4 xx 3 xx 2 xx 1)`
`= - 15 xx 7 xx 13 - 1365`
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