Permutations with and without Repetition
A permutation is an ordered arrangement; n distinct objects taken r at a time give nPr = n!/(n-r)! arrangements.
What is Permutations with and without Repetition?
A permutation is an ordered arrangement; n distinct objects taken r at a time give nPr = n!/(n-r)! arrangements.
Key formula / rule: nPr = n!/(n-r)! when repetition is not allowed.
Key points
- Compute the number of permutations in a stated arrangement problem.
- Classify a counting situation as ordered or unordered.
Common exam trap
Counting circular arrangements as if they were linear.
Definitions
- Term
Permutations with and without Repetition
- Meaning
A permutation is an ordered arrangement; n distinct objects taken r at a time give nPr = n!/(n-r)! arrangements.
- Term
Permutations with and without Repetition — explanation
- Meaning
Counting begins with deciding whether order matters and whether repetition is allowed. Fixing those two answers first prevents almost every counting error.
Learning objectives
Compute the number of permutations in a stated arrangement problem.
Classify a counting situation as ordered or unordered.
Formulae
- Key point
nPr = n!/(n-r)! when repetition is not allowed.
- Key point
With repetition allowed the count is nr.
- Key point
Arrangements of n objects with repeats divide by the factorials of the repeat counts.
Common mistakes
Counting circular arrangements as if they were linear.
Forgetting to divide by repeats when identical objects are present.
Keywords
Permutations
with
without
Repetition
Practice preview
How many distinct 4-letter words can be formed using the letters of the word 'MATH' if each letter is used exactly once?…
easy
How many different arrangements can be made from the letters of the word 'APPLE'?…
easy
In how many ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?…
medium