Question

How many ways can you listen to 3 songs from a cd that has 12 selections?

Answer 1

Taking into account the definition of permutation, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.

What is permutation

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:

$P=\frac{m!}{(m-n)!}$

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.

Number of ways you can listen to 3 songs

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:

$P=\frac{12!}{(12-3)!}$

$P=\frac{12!}{9!}$

$P=\frac{479001600}{362880}$

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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