Selections with Repetitions Examples1

In this class, We discuss Selections with Repetitions Examples1.

The reader should have prior knowledge of combinations with repetitions. Click Here.

The examples which we discuss are different from those discussed in previous classes.

These examples are based on limited repetitions.

Example 1:

Take an example: X, X, Y, Z.

From the four characters, we need to select two characters.

How many possible ways to select?

Solution:

The possible ways to select are shown below.

1) Two same characters

2) Two different characters.

Two same characters. We have one possible way.

Two different characters:

We have three different characters X, Y, Z.

We can select two out of three characters in 3C2 ways.

The total possible ways are 1+ 3c2 = 4.

Example 2:

Given X, X, Y, Z, A, B.

How many different three-character selections out of six characters?

Solution:

Different possibilities are given below.

Three different characters.

Two same and one different character

Three same characters.

Three different characters in 5c3 ways.

Two same and one different character in 1 * 4C1 ways.

Three same characters in zero ways.

The total possible ways are 5c3 + 4c1.