Jessica has been given a list of
4 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?
Assuming the favourite and second favourite bands are distinct (different), then there are four choices for the favourite band, and (4-1)=3 choices for the second favourite band.
Use the multiplication rule to find the number of possible votes.
To determine the number of different votes possible, we need to calculate the number of ways Jessica can choose her favorite and second favorite bands from the list of 4 bands.
First, Jessica can choose her favorite band in 4 ways.
After choosing her favorite band, she must then choose her second favorite band from the remaining 3 bands. She can do this in 3 ways.
Therefore, the total number of different votes possible is 4 x 3 = 12.
To determine the number of different votes possible, we need to consider the number of options Jessica has for her favorite band and her second favorite band.
Let's start with the favorite band. There are 4 bands on the list, so Jessica has 4 options to choose from for her favorite band.
Now, for her second favorite band, there are 3 remaining bands to choose from since she already chose her favorite band. Therefore, she has 3 options for her second favorite band.
To find the total number of different votes possible, we multiply the number of options for each choice together. So, Jessica has 4 options for her favorite band and 3 options for her second favorite band. Multiplying these together gives us:
4 (options for favorite band) x 3 (options for second favorite band) = 12
Therefore, there are 12 different votes possible.