Permutations Calculator 
This program computes the total count of possible permutations (unique ordered sequences) of (N) distinct objects if taken in groups of (R) at a time.
NOTE: Since the program performs all of its computations in arbitraryprecision, in some cases, the values of the permutations could extend out to tens of thousands of digits, so it could possibly take up to several seconds to return the computed result. The EXACT value of P(1, 1) is computed below and consists of 1 digit.
Processing time was 0.000027 sec. Jay Tanner  2017

Permutations are ordered sequences, so the number of permutations means the number of unique ordered sequences in which (R) distinct items may be drawn from a total pool of (N) distinct items. For example we could compute the total number of possible unique numbers we could create using 5 different digits from a pool of N unique digits.
All permutations of unique items are unique sequences. Any two sets containing the same (R) items, such as a sequence of numerical digits, are considered identical only if all the digits in both numbers were selected in the same order as well. The symbols are not limited only to numerical digits, they can be letters or any other unique objects as well. The number 12345 is only identical to 12345 and no other permutations of the same digits. Below is a listing of the PHP function at the heart of the above Permutations Calculator program. It computes the total number of possible unique sequences (permutations) in arbitraryprecision, which could extend out to several thousands of digits. /* =========================================================================== This function returns the permutations of (N) items selected (R) at a time. The sequential order of the items in each group is important. Author : Jay Tanner 2014 Language : PHP v5.4.7 =========================================================================== */ function bcPerm_N_R ($N, $R) { $P=1; for ($i=0; $i < $R; $i++) { $P = bcmul($P, $N$i); } return $P; } Jay Tanner  2017
