Permutations with Repetition
Given a set of n elements, the permutations with repetition are different groups formed by the k elements of a subset such that:
The order of the elements does matter.
The elements are repeated.
The permutations with repetition are denoted by PR(n,k).
Permutations with repetition of n elements are permuations where the first element is repeated a times, the second b times, the third c times, ...
n = a + b + c + ...
Examples
1. How many three digit numbers can be formed with the digits: 1, 2, 3, 4, 5?
n = 5 k = 3
The order of the elements does matter.
The elements are repeated.
2. How many three digit numbers can be formed with the digits: 0, 1, 2, 3, 4, 5?
n = 6 k = 3
The numbers must be separated into two blocks:
The first set, of one number, can occupy only one of 5 digits because a number does not begin with zero (except for license plates and other special cases).
n = 5 k = 1
The second block, of two numbers, can occupy any digit.
n = 6 k = 2
3. How many nine-digit numbers can be formed with the numbers 2, 2, 2, 3, 3, 3, 3, 4, 4?
n = 9 a = 3 b = 4 c = 2 a + b + c = 9
The order of the elements does matter.
The elements are repeated.
4. The signal mast of a ship can raise nine flags at one time (three red, two blue and four green). How many different signals can be communicated by the placement of these nine flags?
n = 9 r = 3 b = 2 g = 4 r + b + g = 9
The order of the elements does matter.
The elements are repeated.
