Page 11 - 3_Dinda Erliananda_Counting Principles

Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

Answer:

n= 4 i.e. {1, 2, 3, 4}
P(4, 4) = 4! = 4·3·2.1 = 24.

So, there are 24 vehicles.

3. Permutations with Some Different Elements

Permutations P(n, n) as in the example above shows that from the n available
elements, all of them are taken to be arranged. From n elements, an arrangement with

only r elements can also be made, taking into account the order.

We can write the three members of the set { } into 24 sequences as
follows.

Each sequence or arrangement of the letters is called a set permutation
{ }.

A permutation is an arbitrary arrangement of the elements of a set in order.

The number of permutations obtained from filling places.

Theorem 2

The number of permutations of r elements taken from n different elements is for
.

read permutation level r of n.

Proof (1):

In a set, the number of permutations of r elements taken from n different elements is
written with the notation . or nPr.

( )

( )

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