Dividing people or distinct objects into groups

Calculating number of ways of dividing people or distinct objects into groups of the same size often pose difficulty to students.

Hopefully these examples will help students understand the concept.

Basic Example

How many ways can 10 children be divided into two groups of 5?

1

When dividing people or distinct objects into groups, if p groups are indistinguishable, we need to divide by p! to avoid double counting.

Challenging example 1 

At a particular reception, 9 guests are to stand at 3 identical round tables. How many ways can this be done if there are at least two people at each table?

3

Challenging example 2 (SAJC 2011/MYCT/2/6)

2

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