Permutations Definition and Theorems

Each of the arrangement which can be made by taking some or all of a number of things is called a permutation.



Theorem 1

Let r and n be positive integers such that 1≤r≤n. then the number of all permutations of n distinct things taken r at a time is given by

n(n-1)(n-2)…(n-(r-1))

Notation: Let r and n be positive integers such that 1≤r≤n. then the number of all permutations of n distinct things taken r at a time is denoted by the symbol P(n,r) or ⁿ C_r.

Then P(n,r) = ⁿ C_r = n(n-1)(n-2)…(n-(r-1))


Theorem 2

P(n,r) = ⁿ C_r = n!/(n-r)!

Theorem 3

The number of all permutations of n distinct things taken all at a time is n!.

Theorem 4

0! = 1