Problems Problem

Arrange 6 Books On a Shelf

You have 6 different books and 6 spaces on a shelf. How many shelf orders are possible?

Decision guide

Why this formula fits

This is a factorial or full permutation problem because all 6 distinct books are arranged in a row.

Does order matter? Order matters because swapping two books changes the shelf order.

Is repetition allowed? Repetition is not allowed because each physical book can appear only once.

Worked solution

6! is 720.

  1. Input: n = 6
  2. Formula: n!
  3. Substitute: 6!
  4. Steps: multiply every whole number from 1 through 6
  5. Result: 6! is 720.

Interactive tool

Run the same scenario in the calculator

This is a factorial or full permutation problem because all 6 distinct books are arranged in a row.

Result

0

Enter values to calculate.

What your result means

The explanation updates with the current inputs.

Live visual

Fruit preview

Previewing a small sample keeps the page fast and readable.

Calculation work