Question

Rafeal has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?

Answer 1

Answer: 60 different votes are possible

Explanation:

We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.

The formula for permutations is:

`nPr=(n!)/((n-r)!)`

Where n is the number of bands you can choose and you choose 3 of them.

Then we calculate:

`5P3 =(5!)/((5-3)!)\\\\5P3=(5!)/(2!)\\\\5P3 = 60`

Finally, the number of possible votes is 60

Answer 2

60 different votes.

Explanation:

This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:

5P3 = 5*4*3 = 60 possibilities.

There are 60 different votes!!!