Basics for Enumerative Combinatorics

Basics of Enumerative Combinatorics

Enumerative Combinatorics is…

Number of ways to arrange n objects

Imagine first choosing which object will be at the start of the sequence. There will be $n$ choices.

After choosing the first, there are $n-1$ choices remaining for the second object.

The choices for each object become: $n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 2\times 1$.

Therefore, the number of ways to arrange n objects is $n\times (n-1)\times (n-2)\times \cdots \times 2\times 1$.

So the number of ways to arrange n object is $n!$.