Permutations Vs Combinations

Permutations Vs Combinations

19 October 2008 No Comment

Every one of us should have a clear idea about what is permutation and what is combination. I insist on saying this only because i have seen many people using these two words interchangeably. Let us understand the difference between permutation and combination though an example.

Suppose you want to unlock a number lock and let the unlock code be 1234. OK, now u want to unlock your baggage and u know that the unlock code contains the numbers 1,2,3 and 4 and u r not sure about the exact number.Well,as you all know, only if u set the exact number only, you will be able to open your bag.so, the order of the constituent numbers is important.This condition is what you cal the permutation. That is, the position of numbers is having the utmost importance. I think you get the idea. u will be trying the different combinations of numbers 1,2,3 and 4 to unlock your bag.These different trials are the different permutations.

Now, take another example.Suppose we want to elect a girl and a boy from a class of some 60 students.It doesn’t matter if we elect the girl or the boy first, rite? Suppose a girl named ‘christina’ is elected first and then a boy called ‘Ram’ elected second. Now, a second chance is that we elect the boy(Ram) first and then the girl(Christina). So, it doesn’t matter if we elect the girl or the boy first,rite?That is,the only thing that counts is the elected students and not the order of election. The final outcome is concerned only with the two student representatives and not the order in which they are elected.This is the situation where you use combinations.

Suppose we want to select 2 numbers from 8,9 and 10. The different combinations are (8,9),(9,10), and (8,10).The corresponding permutations are (8,9),(9,10),(8,10),(9,8),(10,9), and (10,8).That is,the order of selection is also a matter of concern and thus (8,9) and (9,8) are different.

As a concluding point, we can say that permuatation concerns with the position and combination concerns only with the chosen objects.