Question

Martina has been given a list of 5 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?

Answer 1

Explanation:

Martina has been given 5 bands and asked to place a vote for her favorite and second favorite bands. The number of different votes possible can be calculated using combinations.

A combination is a way of selecting items from a set, where order does not matter and repetition is not allowed. To find the number of combinations, we can use the formula:

C(n, k) = n! / (k! * (n - k)!)

where:

n is the number of items

k is the number of items being selected

! denotes factorial, which is the product of all positive integers up to that number

Step-by-step, the calculation is as follows:

Determine the number of items and the number of items being selected:

n = 5 (the number of bands)

k = 2 (the number of bands Martina is voting for)

Calculate the number of combinations using the formula:

C(n, k) = n! / (k! * (n - k)!)

C(5, 2) = 5! / (2! * (5 - 2)!)

C(5, 2) = 120 / (2 * 3!)

C(5, 2) = 120 / (2 * 6)

C(5, 2) = 120 / 12

C(5, 2) = 10

So, there are 10 different votes possible for Martina's favorite and second favorite bands from the list of 5 bands.