# Combinations and Permutations

## Combinations and Permutations

Permutation and combination related questions are common in PSC and Bank exams.

Before going to Combinations and Permutations, first lean about factorial.

If \'n\' is a positive integer then, factorial of n is denoted as n!.

5! = ( 1 x 2 x 3 x 4 x 5 ) = 120

4! = (1 x 2 x 3 x 4 ) = 24

Permutations are for lists of items, whose order matters and combinations are for group of items where order doesn’t matter. in other words,

• When the order of items doesn\'t matter, it is called as Combination.
• When the order of items does matter it is called as Permutation.

The number of permutations of n objects taken r at a time is determined by using this formula:

P(n,r)=n!/(n−r)!

Permutation: Listing your 3 favourite football team in order, from list of 10 teams. P(10,3) = 720.

The number of combinations of n objects taken r at a time is determined by using this formula:

C(n,r)=n!/((n−r)!r!)

Combination: Picking a team of 3 people from a football coaching group of 10. C(10,3) = 10!(3!(10−3)!) = 120.

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