Permutation & Combination

Combination & Permutation deals with arrangement of thing. If the order doesn't matter, then it is called Combination. If the order does matter, then it is a Permutation.

In other words, Permutation is an ordered Combination.

Permutation

nPr = n!/(n-r)!

There are basically two types of permutation:

  1. When repetition is allowed
  2. No repetition

1. Permutations with Repetition

To choose r things from n when repetition is allowed, the permutations are:

n × n × ... (r times) = nr

(Because there are n possibilities for the first choice, then there are n possibilities for the second choice, and so on.)

Combinations

Number of ways objects can be selected from a group.

nCr = nPr / r!

Circular Permutations

Circular Table

A circular table has no fixed starting or ending point. If n persons are to be arranged in a straight line, there are n! unique ways. When n persons are to sit around a circular table, each arrangement will be repeated n times, There will be (n-1)! different arrangements.

Circular Wire

Arrangement of beads (which are all different) around a circular wire differs from table. Why? Because when you turn it over, you can see other side of it like a mirror image. So, total number of different arrangements decreases by half. Thus, n beads on a circular wire can be arranged in (n-1)!/2 ways.