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 General Aptitude
 Permutation and Combination
 Important Formulas
1.  Factorial Notation:  
Let n be a positive integer. Then, factorial n, denoted n! is defined as:  


Examples:  


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


3.  Number of Permutations:  
Number of all permutations of n things, taken r at a time, is given by:  


Examples:  


4.  An Important Result:  
If there are n subjects of which p_{1} are alike of one kind; p_{2} are alike of another kind; p_{3} are alike of third kind and so on and p_{r} are alike of r^{th} kind, such that (p_{1} + p_{2} + ... p_{r}) = n. 



5.  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.  
Examples:  


6.  Number of Combinations:  
The number of all combinations of n things, taken r at a time is:  


Note:  


Examples:  
