Table of Contents
A fundamental counting principle

If Task A can be performed in any one of x ways, and if, after Task A is performed, Task B can be performed in any one of y ways, then the combination tasks, A followed by B, can be performed in x·y ways.

Arranging the letters in the name "FRED".

Four ways to pick the first letter, then three ways to choose the second letter, then two ways to choose the third letter: a total of 4·3·2 = 24 arrangements (in yellow below).

F         
FR         
FRE        FRED
FRD FRDE
FE 
FER        FERD
FED FEDR
FD 
FDE        FDER
FDR FDRE
RF         
RFE        RFED
RFD RFDE
RE
REF        REFD
RED REDF
RD
RDF        RDFE
RDE RDEF
E
EF         
EFR         EFRD
EFD EFDR
ER
ERF         ERFD
ERD ERDF
ED
EDF         EDFR
EDR EDRF
D
DF         
DFR        DFRE
DFE DFER
DR
DRF        DRFE
DRE DREF
DE
DEF        DEFR
DER DERF