Permutations
When the elements of a set are arranged in a definite order, the arrangement is called a permutation of the elements. The number of permutations of n objects is n!
The number of possible orderings of m objects taken from a set of n is given by:
nPm = n × (n – 1) × (n – 2) × · · · × (n – m + 1)
= 
That is, count backwards starting from n, writing down the numbers as you count, until you've written down m numbers. Then multiply them all together.
Example:
Suppose you're a television programmer, and you have five half-hour shows to choose from, but only three time slots. How many different programs are possible?
Using the permutations formula, we have:
5P3 = 5 × 4 × 3 = 60
To see why this works, name the shows A, B, C, D, and E, and make a list:
ABC ABD ABE ACB ACD ACE ADB ADC ADE AEB AEC AED |
BAC BAD BAE BCA BCD BCE BDA BDC BDE BAC BAD BAE |
CAB CAD CAE CBA CBD CBE CDA CDB CDE CEA CEB CED |
DAB DAC DAE DBA DBC DBE DCA DCB DCE DEA DEB DEC |
EAB EAC EAD EBA EBC EBD ECA ECB ECD EDA EDB EDC |
In this case, there are 5 choices for the first program, 4 choices for the second program, and 3 choices for the last program. So the answer is:
5P3 = 5 × 4 × 3 = 60
If there were 8 programs and 4 time slots, we would have:
8P4 = 8 × 7 × 6 × 5 = 1680
