Permutation

Problem
In how many ways can the letters of the word MATHALINO be arranged if the vowels are to come together?
 

Problem
In how many ways can the letters of the word MATHEMATICS be arranged if the consonants are to come together?
 

Fundamental Principle of Counting
If event E₁ can have n₁ different outcomes, event E₂ can have n₂ different outcomes, ..., and event E_m can have n_m different outcomes, then it follows that the number of possible outcomes in which composite events E₁, E₂, ..., E_m can have is

We call this The Multiplication Principle.