Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

Permutations refer to the different ways in which a set of items can be arranged or ordered. In mathematics, the number of permutations of 'n' items taken 'r' at a time is calculated using the formula P(n, r) = n! / (n - r)!, where 'n!' denotes the factorial of 'n'. This concept is crucial for understanding how to count arrangements when the order of selection matters.

A factorial, denoted as 'n!', is the product of all positive integers up to 'n'. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are fundamental in combinatorics, particularly in calculating permutations and combinations, as they provide a way to quantify the total arrangements of a set of items.

The distinction between combinations and permutations is essential in combinatorial mathematics. While permutations consider the order of selection (e.g., ABC is different from ACB), combinations focus solely on the selection itself, disregarding order (e.g., ABC is the same as ACB). Understanding this difference is vital when determining which formula to apply in problems involving arrangements.