Page 14 - 3_Dinda Erliananda_Counting Principles

Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

(i) the same elements are not distinguished, and

(ii)

Theorem 3
The number of ways to divide n elements into k cells, each containing an element in the

first cell, an element in the second cell, and so on until the element in the k cell

is:

Example 6:
Determine the permutations of the elements { }!
Answer:
If S = { }, then

= 6 (number of examples (members) of the set )

= 2 (many letters )
= 3 (many letters )

= 1 (many letters )

so the number of permutations is:( ) .

Example 7:

In how many ways can 4 red balls, 3 white balls, and 1 yellow ball be arranged in a
row, if the balls of the same color are indistinguishable from each other.

Answer:
There are 8 balls consisting of 4 red, 3 white and 1 yellow.

Many different ways = ( ) method or 280 ways.

So, there are 280 different ways to arrange the balls in a row.

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