Fundamental principle of counting is also known as multiplication principle.
Principle
If an event can occur in m different ways, following which another event
can occur in n different ways, then the total number of occurrence of the events in the given order is m×n.
The above principle can be generalised for any finite number of events. For
example, for 3 events, the principle is as follows.
If an event can occur in m different ways, following which another event can occur in n different ways, following which a third event can occur in p different ways, then the total number of occurrence to ‘the events in the given order is m × n × p.
Example
Find the number of 5 letter words, with or without meaning, which can be
formed out of the letters of the word REKHA, where the repetition of the letters is not allowed.
By multiplication principles, the words can be formed in 120 ways.
NOTE: With repetition
If the repetition was allowed, it can be formed 5 x 5 x 5 x 5 x 5 = 3125 ways.