University Mathematics Handbook (2015)

XV. Combinatorics and Newton's Binomial

Chapter 1. Permutations

1.1  Permutations without Repetition

a. A permutation in distinct objects (elements) is their possible arrangement in a line.

b. The difference between permutation in distinct objects and another permutation of the same objects is in the order of its terms.

c. The total number of permutations of objects is:

, (n-factorial)

d. The number of circular, or cyclic, permutations is the number of all possible rearrangements of distinct elements in a circle.

It is

1.2  Permutations with Repetition

a.  A permutation with repetition is the linear arrangement of objects, when objects are similar, another objects are similar, and the remaining are similar, and when . It is denoted .

b.