Permutations and Combinations all concept in one place


Factorial notation is !

n! = n(n-1)(n-2)(n-3)........3.2.1

Eg:- 4! = 4*3*2*1

        5! = 5*4*3*2*1

        0! = 1


nPr = n!/(n-r)!

In permutations with a,b,c is (ab, ba, ac, ca, bc, cb) 

Number of all permutations of n things , taken all at a time = n!

If there are n objects of which p1 are alike of one kind , p2 are alike of another kind, p3 are alike of third kind and so on and Pr are alike of rth kind such that (P1+P2+.........+Pr)= n

Then number of permutations of these n objects is:  n!/(P1!)(P2!)...(Pr!)


nCr = n!/(r!)(n-r)!

Note that :  nCn = 1 and nC0 = 1 .

An Important :  nCr = nC(n-r)

In combinations with a,b,c is only (abc)

NOTE:- ab and ba are two different permutations but they are same in combinations

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