Taking into account the definition of permutation, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.
<h3>What is permutation</h3>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:
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.
<h3>Number of ways you can listen to 3 songs</h3>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:
- m=12
- n=3
and replacing in the expression for permutation, you get:
<u><em>P= 1320</em></u>
Finally, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.
Learn more about permutation: