Coefficient of $x^{3}$ in the expansion of $e^{- bx}$

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$\frac{b^{3}}{3}$

$\frac{- b^{3}}{6}$

$\frac{- b^{3}}{3}$

$\frac{b^{3}}{6}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} e^{- bx} \\ = & 1 - bx + \frac{{(bx)}^{2}}{2} - \frac{{(bx)}^{3}}{3} + \dots \dots \dots \\ x^{3} coef & = & \frac{- b^{3}}{3} = \frac{- b^{3}}{6} \end{array}$

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