gen-define-counting-with-repetition-and-give-one-short-worked-ex-7d29

Define counting with repetition and give one short worked example.

# Counting with Repetition **Definition:** Counting with repetition refers to counting arrangements where items can be selected multiple times from a set. The key formula is: **For selecting r items from n types (with repetition allowed):** n^r This applies when: - Order matters - Items can be reused - Each position has the full set of choices available --- ## Worked Example **Problem:** How many 3-digit PIN codes can be formed using digits 0-9? **Solution:** - We have n = 10 digits (0,1,2,3,4,5,6,7,8,9) - We need to select r = 3 positions - Digits can repeat (like 111, 222, etc.) Number of PIN codes = 10³ = **1,000** (Each position has 10 choices: 10 × 10 × 10 = 1,000)