Use the Given Information to Find the Exact Value of the Expression

Multiple Choice

Use the given information to find the exact value of the expression.
- $\sin \alpha = - \frac { 24 } { 25 } , \alpha$ lies in quadrant IV, and $\cos \beta = - \frac { \sqrt { 21 } } { 5 } , \beta$ lies in quadrant III Find $\sin ( \alpha - \beta )$ .

A) $\frac { 14 + 24 \sqrt { 21 } } { 125 }$
B) $\frac { - 14 + 24 \sqrt { 21 } } { 125 }$
C) $\frac { - 48 + 7 \sqrt { 21 } } { 125 }$
D) $\frac { - 48 - 7 \sqrt { 21 } } { 125 }$