Combinatorics Worksheets 🖨️
The Art of Counting: Mastering Combinatorics
1. Factorials (!)
A factorial means multiplying a number by every whole number below it down to 1. For example, $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. It represents the total number of ways to arrange a set of items.
2. Permutations (P)
Used when order matters. If you are choosing $r$ items from a pool of $n$ items and arranging them (like picking a 1st, 2nd, and 3rd place winner), you use $^nP_r$.
Formula: $\frac{n!}{(n-r)!}$
3. Combinations (C)
Used when order does not matter. If you are just choosing a group of $r$ items from a pool of $n$ items (like picking 3 people for a team), you use $^nC_r$.
Formula: $\frac{n!}{r!(n-r)!}$