Page 10 - 3_Dinda Erliananda_Counting Principles

Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

2. Permutations with All Different Elements

Definition: Permutation
Permutations are different arrangements that can be formed from n elements, which are

taken from n elements or some elements.

Theorem 1

If there are n different elements, n elements are taken, then the number of different
arrangements (permutations) of these n elements is

 nPn, reads the nth level permutations of n elements.



Proof:

Suppose it is known that n pieces will not be arranged in n non-circular places.
The first place is filled in n ways because there are n elements. The 2nd place is filled in a

way because an element has been filled in the first place, the 3rd place is filled in

ways and so on until the 2nd place – is filled in 2 ways and the nth (last)
place is filled in 1 way.

place to- Number of Ways

1 n
2 n– 1

3 n– 2
4 n– 3

5 n– 4

n –2 3

n– 1 2
n 1

Overall the many ways to create different arrays (permutations) are:

Example 4:
How many vehicles can be assigned a license plate that uses the symbols of the numbers 1,

2, 3, 4, and there is a repeating symbol in each number consisting of 4 digits?

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