Question

Hong has been given a list of 6 bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?

Answer 1

This requires us to find the number of permutations of 6 different bands taken 2 at a time:
$6P2=\frac{6!}{(6-2)!}=30\ different\ votes.$