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.

To find the number of ways Tim can listen to 3 songs from an album of 11 songs, we use the permutations formula \( _{n}P_{r}=\frac{n!}{(n-r)!} \). Here, \( n = 11 \) and \( r = 3 \). So, substituting the values: \[ _{n} P_{r} = \frac{11!}{(11-3)!} = \frac{11!}{8!} \] This simplifies to: \[ 11 \times 10 \times 9 = 990 \] There can be 990 ways to listen to the 3 songs. And as a fun fact, did you know that the art of permutations dates back to ancient civilizations? Mathematicians like the Greeks and Indians would study arrangements and combinations, laying the groundwork for modern probability and statistics! If you're interested in diving deeper into the world of permutations and combinations, a great read is "The Art of Combinatorial Mathematics" by John H. Conway. This book is not only eye-opening but also enhances your understanding of counting methods with insightful problems and elegant solutions!