Answer
Number of ways that the director cast the role = $8_{{P}{_{3}}}$ = 336
Work Step by Step
Total number of actors = 8
Number roles (Tony, Riff, Bernardo) = 3
Number of ways that the director cast the role = $8_{{P}{_{3}}}$ = $\frac{8!}{(8 - 3)! }$ = $\frac{8!}{5! }$
= $\frac{8\times7\times6\times5!}{5! }$
= $8\times7\times6$
= 336
