Suppose you are asked to list, in order of preference, your five favorite albums you purchased in the past 12 months. if you bought 20 albums over this time period, in how many ways can the five favorites be ranked?

Question

Thunder Thighs

Mathematics

7 September, 18:38

Suppose you are asked to list, in order of preference, your five favorite albums you purchased in the past 12 months. if you bought 20 albums over this time period, in how many ways can the five favorites be ranked?

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Justice Chung · Answer 1

When the order doesn't matter, we would be using the Combination. While, when the order does matter it is called permutation.

In this case, permutation would be use since there is a ranking for the albums.

We need to choose and arrange 5 albums out of 20. Hence, the number of possible ways will be:

5/20 P = 20! Divided by (20 - 5) ! = 20 x 19 x 18 x 17 x 16 = 1860480