Combinations and Permutations Combinations and Permutations Before studying probability you need to have good knowledge of permutation and combination. Permutation and combination is two different things, and most of the student is not able to find the difference between these two terms, today we will be explaining both permutation and combination separately so that you will be able to differentiate between the two. Before studying permutation and combination you need to have the knowledge of factorial, so firstly we will be studying factorial then we will be moving to permutation. We denote factorial by “!” Sign, if we have n positive integer, then factorial n will be defined as n! = n(n - 1)*(n -2)*(n-3)………3.2.1 Suppose if we are asked to find the factorial of 4 then it would be 4*3*2*1 = 24, in the same way we can find the factorial of any given number now we will move to permutation. Permutation can be defined as “the different arrangements of a given number of things by taking some or all at a time is called as permutation”. We will use permutation when we have small data.
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If we take an example then we can say that all the permutation (or arrangement) made with the letter a ,b ,c by taking two at a time will be ab, ba,ac,ca,bc,cb, so these are the six permutation that will be made by these letter. If we again find the permutation made by the letter a,b,c but this time we will take three at a time , then possible permutation will be ,abc,acb,bca,bac,cab,cba. We can also define a formula for permutation as npr = n!/ (n-r)! Here n is the total number of things and r is the things that we take at a time Suppose there are 6 books and we have to select only two so number of permutation will be 6p2 in this way we can find the permutation of any given data, now there is is a very important rule which we need to remember is if there are n object of p1 , are alike of one kind , p2 is alike of other kind, p3 is alike of other kind and so on and pr are alike of r kind such that p1 +p2 +p3………. + pr = n , then number of permutation of n object is n!/(p1! *p2...*pr!) now we will move to combination, each of the different group or selections which can be formed by taking some or all of a number of object then it is called as combination , we use combination for bigger data. If we take a example in which we need to select 2 boys out of three boys A, B,C then possible selection are AB,BC,CA, now you are thinking why we are not taking BA,CB,AC just because AB and BA represent the same selection.
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If we have to form a combination by a,b,c taking three at a time then it will be abc only .we denote combination by C and formula for the combination is given below, ncr = n!/r!(n-r)! Here n is the total number of things and r is the things that we take at a time There are two important point that we need to remember is that ncn = 1 and nc0 = 1 This is all about permutation and combination
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