Page 16 - 3_Dinda Erliananda_Counting Principles

Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

 If 2 people are always together, then there is a way they sit.

 If the 2 people were assumed to be one person, then there are 6 people who
want to sit around the table, then there are:

method.

So, the number of ways 7 people can sit around a table is a way.
ways.

C COMBINATION

If we have a set of data mutated two or two of the three elements,
namely , the arrangement of the permutations is 6 as follows:

Assuming that , and .

For example, , means that the tens number that can be
composed of the set of numbers {1, 2, 3} is:

12, 13, 23,

21, 31, 32
However, it would be very different if = Ali, = Bahrun, = Chalid, meaning that

the data set S = {a, b, c} is a collection of people's names. The two-by-two permutations of
the three elements are where .

The difference in the number of permutations above is only a matter of "with" or

"without" considering the arrangement.
So,

(i) the two-by-two permutations of the three elements {a, b, c} "with respect to the order"

are , and .
(ii) the two-by-two permutations of the three elements {a, b, c} "regardless of order" are

.
A permutation "regardless of the order chosen" is called a combination. In the case

example above, the permutation of 2 elements from 3 elements that are known "without"

paying attention to the order is written with symbols (3, 2) or or( ).

So, the number of combinations of 2 elements out of 3 elements is C(3, 2) = 3.

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