Enter number of different objects ( 1 to 150 ):
Enter size of groups taken from objects ( 1 to number above ):

For example, if we have 20 puzzle squares that make a Colorado mountain scene at above left, then how many possible ways could we place the pieces in random ways in the puzzle to get the randomized image at the above right? To get the answer: enter 20 in the "number of different objects" box, enter 20 in the "size of groups" box, and then click "Calculate Permutations".
The answer is really a large number, 2,432,902,008,176,640,000 ways or in other words, either image, left or right, will occur on average once in two thousand four hundred thirty two trillion times! The puzzle at the above right will be different next time you come here, or you can "Randomize" the puzzle here:

Note: The formula for permutations of n different objects taken r at a time with attention given to the order of arrangement is denoted by nPr or Pn,r or P(n,r) = n!/(n-r)! where the symbol "!" stands for "factorial". For example, 5! means 5*4*3*2*1 = 120. Thus, in the example above we have 20!/(20-20)!, but don't forget that 0! is 1 so we really have 20!/1 or 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 which equals, I hope, 2,432,902,008,176,640,000 - a truly astounding number. In fact, we as humans (I'm assuming you are one) can probably not comprehend such a number. For instance, if we say a USA quarter is 2.4 cm in diameter and a Swedish crown (krona) is 2.5 cm in diameter (my measurements) then how many times around the world will 2,432,902,008,176,640,000 coins of each type go? Well...click here to find the answer
Or how many times will this number of quarters or Swedish crowns cover the entire surface of the earth?
JavaScript © 2000 by John A. Byers Chemical Ecology