Answer: 8
Step-by-step explanation:
The number of permutations of n items taken m at a time is given by the following formula:
[tex]P(n,m)=\dfrac{n!}{(n-m)!}[/tex] (here order matters)
Here the couple need to select 7 routines out of 8 to perform in an order.
So, the number of ways to arrange that = [tex]P(8,7)=\dfrac{8!}{7!}=\dfrac{8\times7!}{7!}=8[/tex]
Hence, the number of different ways to arrange their performance = 8
