Nicole has been given a list of 3 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?
What kind of school SUBJECT is Strayer?
I hope you have not strayed so far from home that you can't get back in time for supper.
To find out how many different votes are possible, we need to understand the concept of combinations.
A combination is a selection of items from a given set, without regard to the order. In this case, Nicole needs to select her favorite and second favorite bands out of the list of 3 bands.
To determine the number of combinations, we can use the formula for combinations:
C(n, r) = n! / (r! * (n-r)!)
Where:
- n is the total number of items in the set (in this case, the number of bands = 3)
- r is the number of items to be selected from the set (Nicole needs to select her favorite and second favorite band, so r = 2)
- n! represents the factorial of n, which is the product of all positive integers from 1 to n
Now, let's calculate the number of different votes possible:
C(3, 2) = 3! / (2! * (3-2)!)
= 3! / (2! * 1!)
= (3 * 2 * 1) / (2 * 1 * 1)
= 6 / 2
= 3
Therefore, there are 3 different votes possible for Nicole, as she can choose any combination of her favorite and second favorite bands from the list.