SOURCE: Don’t Memorise
Permutation and Combination is a mathematical formula used in various ways in which a set of objects are selected and are formed into a subset.
This arranging of subsets is known as permutation when the order is the main factor and combination when the order is not a factor.
Permutation and Combination Formula
The formula of permutation and combination has ‘r’ as an element out of ‘n’ number of elements which is total elements. ‘P’ and ‘C’ are permutation and combination of the objects. Formulas for Permutation and combination is as follows:
n P r = n! / (n – r)!
n C r = n! / [(r !)(n – r)!]
Permutation arranges all the objects accordingly while subsets out of it. There is one easy and tricky way to get the number of letters for which the permutation is required and it is n P n = n! The required formula is mentioned below n P r = n! / (n – r)!
The combination is different from Permutation and it’s formula remains as it is i.e. n C r = n! / [(r !)(n – r)!]
Difference between Permutation and Combination
|The order of elements is taken into consideration||In combination, the order does not matter|
|n P r = n! / (n – r)!||n C r = n! / [(r !)(n – r)!]|
|There are different ways in which a collection of elements can be arranged||Whereas in combination we cannot|
Permutation and Combination Questions
There are various questions solved in this particular chapter and a student needs to learn the trickest way to solve it for various entrances and competitive exams.
There are some various questions for the students with the solution
- There are 7 consonants and 4 vowels. How many words of 3 consonants and 2 vowels can be formed?
Ans. Number of ways of selecting 3 consonants from 7= 7 C3
Number of ways of selecting 2 vowels from 4= 4C2
The total number of ways is 7 C3 x 4C2 = 210
Number of ways of arranging 5 letters is 5! =120
Required number of ways is 210 x 120 = 25200
2. In how many of the ways can a group of 5 men and 2 women be made out of 7 men and 3 women?
Ans. Number of ways of selecting 5 men from 7 = 7C5
Number of ways of selecting 2 women from 3 = 3C2
Required number of ways is by multiplying both the solutions using nCr = nC(n-r) = 63
3. How many 3 letter words with and without meaning can be formed out of the letters of the word BACKGROUND if repetition of letters is not allowed?
Ans. The word has 10 different letters
The number of 3 letter words with and without meaning formed by using these letters = 10P3 = 10 x 9 x 8 = 720