The Different arrangements of a given numbers of things by taking some or all at a time are called permutation.
Factorial notation: Let n be positive integers. Then the factorial of n is denoted by n! And is defined as: n!= n(n-1)(n-2).......3.2.1
(i) 5!= (5*4*3*2*1)=120
Number of all permutations of n things, taken r at a time is given by:
nPr= n(n-1)(n-2)....(n-r+1)= n!/(n-r)!
6P2 = (6*5) = 30
Cor. 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 another kind, P3 are alike of third kind and so on and Pr are alike of rth kind, such as (P1+P2+P3....+Pr) =n.
Thus, number of permutations of these n objects is: