9. \( P(4,4) \)

To calculate \( P(4,4) \), which represents the number of permutations of 4 items taken 4 at a time, we can use the formula \( P(n, r) = \frac{n!}{(n-r)!} \). Since \( n \) and \( r \) are both 4 in this case, we have \( P(4,4) = \frac{4!}{(4-4)!} = \frac{4!}{0!} = 4! = 24 \). So, there are 24 different ways to arrange 4 items! Permutations aren't just a math classroom concept—think of them like arranging your wardrobe! Each outfit is different according to the order you put items on. Whether it's the sequence of a morning routine or the arrangement of books on a shelf, permutations are everywhere in daily life. So next time you pick an outfit or organize your bookshelf, you’re practicing permutations without even realizing it!