Find the Exact Value of the Expression Using the Provided $\sin ( s - t )$

Multiple Choice

Find the exact value of the expression using the provided information.
-Find $\sin ( s - t )$ given that $\cos s = \frac { 1 } { 3 }$ , with $s$ in quadrant $I$ , and $\sin t = - \frac { 1 } { 2 }$ , with $t$ in quadrant IV.

A) $\frac { 2 \sqrt { 6 } - 1 } { 6 }$
B) $\frac { \sqrt { 3 } - 2 \sqrt { 2 } } { 6 }$
C) $\frac { 2 \sqrt { 6 } + 1 } { 6 }$
D) $\frac { \sqrt { 3 } + 2 \sqrt { 2 } } { 6 }$