Permutation Combination

Permutation is the rearrangement of objects or symbols into distinguishable sequences. Each unique ordering is called a permutation. For example, with the numerals one to six, each possible ordering consists of a complete list of the numerals, without repetitions. There are 720 total permutations of these numerals, one of which is: "4, 5, 6, 1, 2, 3". The Order of Items is essential and it concerns selection as well as arrangement. For Example, If there are two objects A and B then the different arrangements are , AB and BA ,thus there are two ways. If there are n objects then the different possible arrangements taking r of them is demoted as ⁿP_r.

ⁿP_r = n!/(n-r)!

0! = 1 and factorials of negative numbers are not defined.

Combination means selection of different items. If there are n things then each of the different selections that can be made taking some or all of n things is called a combination.

The ordering of the items is immaterial and it concerns only selection. For example, if there are two objects A and B, and one has to select both then selecting A first and then B or B first and then A doesn't make any difference in the number of selections. Thus, there is only one way to select both A and B out of them.

If there are n objects then the different possible selections which can be made taking r of them is denoted as ⁿC_r.

ⁿCr = n!/r!(n-r)!

The Golden Rule: If an event A occurs in m different ways and an event B occurs in n different ways then the total number of ways in which both A and B occurs together is m x n.