PERMUTATIONS AND COMBINATIONS
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
Permutations:-
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!)
Combinations:-
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