Permutation Calculator (nPr)

Understanding Permutations

What is a Permutation?

A permutation is an arrangement of objects where order matters. It answers the question: "In how many ways can we arrange a subset of items from a larger set?"

The Permutation Formula

The formula for permutations is:

\[P(n,r) = \frac{n!}{(n-r)!}\]

Where:

• n = total number of items to choose from
• r = number of items being arranged
• ! denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1)

Calculation Steps

To calculate a permutation:

1. Identify n and r
2. Calculate n!
3. Calculate (n-r)!
4. Divide n! by (n-r)!

Example Calculation

Let's calculate 5P3 (permutation of 5 items taken 3 at a time)

\[P(5,3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \times 4 \times 3 \times 2!}{2!} = 5 \times 4 \times 3 = 60\]

Visual Representation

This diagram illustrates the calculation of 5P3, showing how we arrange 3 items from a set of 5.