Carmen's friend made her a CD with 6 songs on it. Carmen decides to put the CD on shuffle and listen to 4 random songs before school. How many sequences of 4 songs are possible?
Question
Carmen's friend made her a CD with 6 songs on it. Carmen decides to put the CD on shuffle and listen to 4 random songs before school. How many sequences of 4 songs are possible?
Solution
This is a permutation problem. Permutations are used when the order of items is important. In this case, the order in which Carmen listens to the songs is important.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
In this case, n = 6 (the total number of songs) and r = 4 (the number of songs Carmen will listen to).
So, the number of permutations is:
P(6, 4) = 6! / (6-4)!
= 654321 / 21
= 720 / 2
= 360
So, there are 360 possible sequences of 4 songs that Carmen can listen to.
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