Answer: 20 different total voting combination
Step-by-step explanation: So we have 5 bands. Lets called them A, B, C, D, and E.
If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.
To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.
Here are the results/totals:
AB
AC
AD
AE
BA
BC
BD
BE
CA
CB
CD
CE
DA
DB
DC
DE
EA
EB
EC
ED
So this is 20 different total voting combinations.
If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.