The number of PERMUTATIONS of 5 things taken 3 at a time is 60.
The number of COMBINATIONS of 5 things taken 3 at a time is 10.
Here's why. Look at the array below. There are 60 things (3-letter
sequences) below but only 10 columns. The 60 things are the 60
permutations. The 10 columns represent the 10 combinations.
1 2 3 4 5 6 7 8 9 10
ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE
ACB ADB AEB ADC AEC AED BDC BEC BED CED
BAC BAD BAE CAD CAE DAE CBD CBE DBE DEC
BCA BDA BEA CDA CEA DEA CDB CEB DEB DCE
CAB DAB EAB DAC EAC EAD DBC EBC EBD ECD
CBA DBA EBA DCA ECA EDA DCB ECB EDB EDC
For instance, take column 7. {BCD,BDC,CBD,CDB,DBC,DCB}.
If you consider all 6 of these as the same thing, then you
are talking about a COMBINation, because the order of the
three letters B, C, and D does not matter to you, i.e.,
BDC is the same as DCB or CDB. But if you consider BDC, DCB
and CDB are three different things, then you are talking about
PERMUTations.
If changing only the order of a group makes a different situation,
then you are talking about permutations. But if changing the order
does not make a different situation, you are talking about
combinations.
If order matters, you are talking PERMUTATIONS. If order doesn't
matter, you are talking COMBINATIONS.
Edwin
