In mathematics, the notion of permutation combination is used in slightly different way from the ordinary meaning. Permutation and combination are the separate words. We can easily differentiate them on the basis of orders, the arrangement of objects. In permutation objects are in some specific order and regarded as the ordered elements while in combination no specified order is there.
We can define permutation as the collection of objects where its order matters in arrangement. We can prove this with the help of an example like UV ≠ VU to understand it in the more precise manner, we will take one more example consider any three names of your friends, suppose Maria(M), George(G), Bob(B). Now the question arises that in how many different ways we can arrange their names. Here we have considered their names as MGB and now we are going to arrange them in the various possible ways, so our result will be MGB, GMB, GBM, BGM, BMG, MBG. Hence conclusion drawn is that there are 6 possible ways to arrange three people.
The possible number of count can also be calculated with the use of formula:
n! = (n) (n-1) (n-2). . . . here the ‘!’ symbol is pronounced as factorial.
Again coming to the above illustration ‘n’ will be considered as three because we have to find the possible number of outcome for three person, now placing the value in the formula:
3! = (3) (2) (1) = 6.
The formula for calculation of permutation is given by P (n, r) = n! / (n-r)!.
Combination is the collection of objects in the different arrangement where the order does not matter and if the order does not matter then we can consider the following UV = VU. Now if we consider the example of Maria, George, Bob then we will not arrange them in the possible number of orders because we have already discussed that in the combination order does not matter. Suppose we want to arrange 5 persons in the group of three then we can easily get the arrangement with the use of the formula. The formula of combination is given below:
C (n, r) = n! / r!(n - r)!,
However the order does not matter we can use this C (5, 3) = 5! / 3! (5 - 3)! = 120 / 12 = 10.
This is all about permutations and combinations.