Taking into account the definition of permutation, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.
Permutations refer to the action of arranging all the members of a set in some kind of order or sequence. This means that if a set is already ordered, the process of rearranging its elements is called permutation.
In other words, permutations of m elements in n positions are the different ways in which the m elements can be arranged occupying only the n positions.
In this case, the elements are not repeated, since if they are repeated or equal to each other, exchanging them does not generate a new permutation. And the order does matter, since the exchange between two different elements generates a new permutation
To obtain the total of ways in which m elements can be placed in n positions, the expression is used:
[tex]P=\frac{m!}{(m-n)!}[/tex]
The sign ! indicates the factorial function, which indicates that all positive integers between the number that appears in the formula and the number 1 must be multiplied.
The order in which songs are listening is important as there is no plan to listen to the same song twice. So, the permutation can be applied.
Being:
and replacing in the expression for permutation, you get:
[tex]P=\frac{12!}{(12-3)!}[/tex]
[tex]P=\frac{12!}{9!}[/tex]
[tex]P=\frac{479001600}{362880}[/tex]
P= 1320
Finally, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.
Learn more about permutation:
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