kay has a playlist of 10 songs. she has time to listen to 4 of the songs on her way to school. how many…

Explanation:

Step1: Identify permutation formula

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be selected and arranged. Here $n = 10$ and $r=4$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So $10! = 10\times9\times8\times7\times6\times5\times4\times3\times2\times1$ and $(10 - 4)!=6!=6\times5\times4\times3\times2\times1$. Then $P(10,4)=\frac{10!}{(10 - 4)!}=\frac{10!}{6!}=\frac{10\times9\times8\times7\times6!}{6!}$.

Step3: Simplify the expression

Cancel out the $6!$ terms. We get $P(10,4)=10\times9\times8\times7 = 5040$.

Answer:

5040