It is the process of selecting 'r' items without replacement from a collection of n items, with the order of the items being important.
The 'combination' is a method of selecting elements from a collection regardless of their order of selection (unlike permutations).
A combination is a selection of 'r' things from a set of ‘n’ items with no replacements and no concern for the order of the items.
Some basic tricks to remember:
– We use permutations if a problem requires you to count the number of different arrangements of things.
– Use combinations if a problem requires many different methods to choose objects, and the selection sequence is not counted.
How many different ways can the letters of the word 'READER' be arranged?
In the word 'READER' contains
Important things to consider while solving permutations and combination problems:
The factorial of any negative quantity is invalid.
– If any work can be done in x ways and another can be done in y ways. then– o Either of the two can be done in x + y different ways.– Both can be accomplished in X × y ways.
Example:
A pair needs to be formed out of a group of 5 bananas. calculate the possible number combinations.