Answer: 120
Step-by-step explanation:
Given : There a six bands competing in a competition.
To find : The number of different ways can the 1st, 2nd, and 3rd place be awarded.
We use permutations here since order matters.
Number of permutation of n things taking r at a time is given by :-
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
For n= 6 and r= 3 , we have the different ways can the 1st, 2nd, and 3rd place be awarded as:
[tex]^6P_3=\dfrac{6!}{(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]
Hence, the 1st, 2nd, and 3rd place can be awarded in 120 ways.
