Combinatorics facts for kids

Combinatorics is a cool part of mathematics. It helps us count and arrange things. Imagine you have a bunch of items, like toys or numbers. Combinatorics helps you figure out how many different ways you can put them together or pick them out. It's all about possibilities and patterns! This field is a big part of discrete mathematics, which deals with separate, distinct items rather than continuous ones.

What is Permutation?

Permutation is a key idea in combinatorics. It helps us solve problems like:

• How many different ways can you put a group of items in order?
• How many ways can you choose some items from a bigger group?

When we think about permutations, a few things can change:

• The items might be all different, or some might be the same.
• The order you pick the items might matter, or it might not.

Permutation Examples

All the possibilities to arrange three differently colored balls

Let's look at some examples to understand permutations better:

• If you have three different colored balls (red, green, blue), there are 6 different ways to arrange them. You can see this in the picture.
• If you have a basket with three identical oranges, there are three ways to pick just one orange.
• If you have a basket with one orange, one apple, and one pear, there's only one way to pick the apple.

Images for kids

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

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  Construction of a Thue–Morse infinite word.

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  Kissing spheres are connected to both coding theory and discrete geometry.

See also

In Spanish: Combinatoria para niños