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 P E R M U T A T I O N S A permutation is the number of different ways in which 'n' objects can be arranged. A good example of a permutation is determining how many ways the letters "ABCD" can be arranged. You could solve this by the "brute force" method and list all possible combinations: ABCD   ABDC   ACBD   ACDB   ADBC   ADCB BACD   BADC   BCAD   BCDA   BDAC   BDCA CABD   CADB   CBAD   CBDA   CDAB   CDBA DABC   DACB   DBAC   DBCA   DCAB   DCBA Although this method works, it is very inefficient and very time-consuming. There is a neater way to do this. If we think of the way these four letters can be arranged, then we know that 4 letters can be in position one, 3 letters can go into position two, 2 letters can go into position three, and 1 letter can go into position four. So the four letters can be arranged in 4 • 3 • 2 • 1 = 24 ways. NOTE: This is also called 4 factorial or 4! An easier way to calculate this is to enter 4 in the calculator and then click "CALCULATE".
 D E R A N G E M E N T S Derangements are another type of combination. This time let us choose "1234" as the example. We know these 4 digits can be arranged in 24 ways but to be considered a derangement, the 1 cannot be in the first position, the 2 cannot be in the second position, the 3 cannot be in the third position and the 4 cannot be in the fourth position. Working within these restrictions, and using the "brute force" method, we find there are 9 possible derangements: 2143   2341   2413 3142   3412   3421 4123   4312   4321 Is there an easier way to count derangements? Yes, and the formula is: