add permutation calculation example

mathematics/permutation_calculation.r

@@ -0,0 +1,21 @@
+# Permutation Calculation
+calculate_permutations <- function(n, r) {
+
+  #' @description Calculates the number of permutations of n objects taken r at a time.
+  #' @param n Total number of objects
+  #' @param r Number of objects in each arrangement
+  #' @usage calculate_permutations(n, r)
+  #' @details Permutations represent the number of ways to arrange r objects from n.
+  #' It is calculated as n! / (n - r)! and is widely used in combinatorics.
+  #' @references https://en.wikipedia.org/wiki/Permutation
+
+  if (r > n) stop("r must be less than or equal to n")
+
+  factorial <- function(x) if (x == 0) 1 else prod(1:x)
+
+  return(factorial(n) / factorial(n - r))
+}
+
+# Example
+print(calculate_permutations(5, 3))  # expected 60
+print(calculate_permutations(10, 2)) # expected 90