How many ways can 4 books be arranged on a shelf?

## The reasoning This is a **permutation problem** — you're arranging distinct items where order matters. Think of filling 4 positions on the shelf, one by one: - **1st position:** You can pick any of the 4 books - **2nd position:** 3 books left to choose from - **3rd position:** 2 books remaining - **4th position:** Only 1 book left So total arrangements = 4 × 3 × 2 × 1 = **24 ways** This is called **4 factorial**, written as **4!** ## Why the wrong options tempt you **Option A (4):** You might think "4 books = 4 ways" — but that's forgetting that *each* first choice opens up more possibilities. **Option B (12):** Maybe you multiplied 4 × 3 and stopped early, forgetting the last two positions. **Option C (16):** This looks like 4², but squaring doesn't apply here — arrangements follow the factorial pattern. ## Quick takeaway **When arranging *n* different items in a line, the answer is always *n*! (n factorial) — multiply all whole numbers from *n* down to 1.**