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Variation

Variations of m elements extracted from n of n

 


Example 1

We take the 4 letters ABCD and start playing with them. If you take all 4 letters there are 24 variations

ABCD   ABDC   ACBD   ACDB   ADCB   ADBC
BACD   BCAD   BADC   BDAC   BCDA   BDCA
CABD   CBAD   CADB   CDAB   CBDA   CDBA
DABC   DACB   DBAC   DBCA   DCAB   DCBA

and calculate this as

With 3 letters there are also 24 variations

ABC   ABD   ACB   ACD   ADC   ADB
BAC   BCA   BAD   BDA   BCD   BDC
CAB   CBA   CAD   CDA   CBD   CDB
DAB   DAC   DBA   DBC   DCA   DCB

and calculate this as

With 2 letters there are 12 variations

AB  AC  AD
BA  BC  BD
CA  CB  CD
DA  DB  DC

and calculate this as

If we take only 1 letter there are 4 variations

A
B
C
D

and calculate this as

For the sake of completeness, we look at what happens if we do not take a single letter. That is by definition also 1 variation

 


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