Combinatorics facts for kids
Combinatorics is a branch of mathematics. It is concerned with finite or countable infinite sets. Combinatorics is part of discrete mathematics. Combinatorics are about graph theory, or Partitions of sets. According to George Pólya, combinatorics looks at counting the number of possibilities, and about the questions whether certain configurations exist, and how to get to them.
Permutation
Permutation is concerned with the following problems:
 Determining how many different ways there are to arrange a number of objects.
 Determining how many ways there are to select a number of objects from a larger set.
There are variations in the problems as follows:
 The objects may or may not be distinguishable.
 The order in which the objects are selected may or may not matter.
Examples
 There are 6 different ways to arrange three distinguishable objects (as shown in the graphic).
 There are three different ways to select one particular orange from a basket with three oranges.
 There is only one possible way to select the apple from a basket that has one orange, one apple and one pear in it.
Images for kids

An example of change ringing (with six bells), one of the earliest nontrivial results in graph theory.

Kissing spheres are connected to both coding theory and discrete geometry.
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Combinatorics Facts for Kids. Kiddle Encyclopedia.