Linear Permutation
Linear Permutation
Permutation
All the possible ways the things can be arranged by using some or all the things are called permutation. Thus each of the arrangements which can be made by taking some or all number of things is called a permutation.
The various ways in which the three things can be arranged by taking two at a time are known as the permutation of three things takes two at a time.
The permutations which can be made by taking the letters a, b and c by taking two at a time are 6 i.e., ab, bc, ac, ba, cb and ca. Each of these presenting a different arrangement of two letters. These six arrangements are called permutations of three things takes two at a time.
Types of Permutation
Permutation is generally of two types
1. Linear permutation
2. Circular permutation
1. Linear Permutation
If the things are arranged in a row/line, then a permutation is called linear permutation. It is simply written as a permutation.
Number of permutations of n dissimilar things taken r at a time is
Where, n! is the product of the first n natural numbers and called n - factorial or factorial n denoted by n!.
e.g., 5! = 5 X 4 X 3 X 3 X 2 X 1 = 120
When n is a negative integer or a fraction, where n! is not defined. Thus, n! is defined only for positive integers.
According to the above definition, 0! makes no sense.
However, we define 0! = 1
For example, The total ways in which the letters of word 'DISCOVER' can be arranged in which all vowels are always together is
Here the total letters are = 8
No of vowels = 3
So in the formula m= 3 and n =8
(because there are 3 vowels)
Find the number of different ways so that the numbers 3, 7, 5 and 9 can be arranged , taking two number at a time. | |||
| Right Option : B | |||
| View Explanation | |||
If P(n , 4) = 20 X P(n , 2) , Find n. | |||
| Right Option : B | |||
| View Explanation | |||
How many four letter words , with or without meaning , can be formed out of the letters of the word , 'LOGARITHMS' , if repetition of letters is not allowed? | |||
| Right Option : A | |||
| View Explanation | |||
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