Page 7 - 3_Dinda Erliananda_Counting Principles

Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

Illustration 2:

set and , then

where = 4 and .

The illustration above shows that: if the first event can be done r different ways
and each of these ways is followed by a second event that can be done s different ways,

then the two events can be done together in different ways. This is called the

Multiplication Rule.
Furthermore, with the multiplication rule, if an event consists of n successive

stages where the first event can be carried out in different ways and each of these ways
is continued by a second event that can be done in a different way, and so on until the

nth event that occurs can be done in different ways, then the event can be carried out

together with the different way.

Example 1:
How many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 without

repetition?
Answer:

To make it easier to answer the question, we create four blank spaces as follows.

To choose a number we can only choose from the numbers 1, 2, 3, 4, 5, and 6. This is
because 0 cannot be placed in the far left position so that the first position can be

occupied in 6 ways (see the following scheme).

If one number has been placed in the first position, then the second position can be
occupied in 6 ways (taken from the number 0 plus the remaining 6 numbers that have

been used in advance).

The third position can be occupied in 5 ways and then the fourth position can be
occupied in 4 ways.

So, the number of numbers that can be arranged is a number.

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