Answer:
Total number of different ways to schedule the appearances is 40320.
Step-by-step explanation:
Total number of performers = 9.
One of the performers insists on being the last stand-up comic of the evening. We have to arrange one performer in last.
\(^1P_1=\frac{1!}{(1-1)!}=\frac{1!}{1}=1\)
We have to arrange the remaining performers. The number of remaining performer is
\(9-1=8\)
Total number of ways to arrange 8 members is
\(^8P_8=\frac{8!}{(8-8)!}=\frac{8!}{1}=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320\)
Total number of ways is
\(40320\times 1=40320\)
Therefore, total number of different ways to schedule the appearances is 40320.
