Arithmatical  Permutations and Combinations
Important facts and Formulae
1.  Factorial Notation: 

Let n be a positive integer. Then, factorial n, denoted n! is defined as: n! = n(n  1)(n  2) ... 3.2.1. 

Example 

5! = (5 x 4 x 3 x 2 x 1) = 120. 
2.  Permutations: 

The different arrangements of a given number of things by taking some or all at a time, are called permutations. 

Example 

All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb). 
3.  Number of Permutations: 

Number of all permutations of n things, taken r at a time, is given by:
^{n}P_{r} = n(n  1)(n  2) ... (n  r + 1) = n!/(nr)! 

Example 

^{6}P_{2} = (6x5)=30 
4.  Combinations: 

Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination. 

Example 

1. Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA 

2. All the combinations formed by a, b, c taking ab, bc, ca. 

3. The only combination that can be formed of three letters a, b, c taken all at a time is abc.
