Question
Use permutations to solve. Tim is a huge fan of country music. If Tim has time to listen to only 3 of the 11 songs on an album, how many ways can he listen to the 3 songs? Substitute values into the formula for \( { }_{n} P_{r} \). \( { }_{n} P_{r}=\frac{\square!}{(\square-\square)!} \) (Type an integer or a decimal.) There can be \( \square \) ways to listen to the 3 songs.
Ask by Sandoval Pollard. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 990 ways to listen to the 3 songs.
Solution
We use the permutation formula for \( n \) items taken \( r \) at a time:
\[
{}_{n}P_{r} = \frac{n!}{(n - r)!}
\]
Substitute \( n = 11 \) and \( r = 3 \):
\[
{}_{11}P_{3} = \frac{11!}{(11 - 3)!} = \frac{11!}{8!}
\]
This simplifies to:
\[
11 \times 10 \times 9 = 990
\]
There are \( 990 \) ways to listen to the 3 songs.
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To determine how many ways Tim can listen to 3 songs from an album of 11 songs, we can use the permutation formula \( { }_{n} P_{r} = \frac{n!}{(n-r)!} \). Here, \( n = 11 \) and \( r = 3 \). Substituting the values into the formula gives us: \( { }_{11} P_{3} = \frac{11!}{(11-3)!} = \frac{11!}{8!} \). Calculating this, we simplify it to: \( 11 \times 10 \times 9 = 990 \). There can be 990 ways to listen to the 3 songs.
