Number Formation with Distinct Digits
Number Formation with Distinct Digits involves forming numbers where digits cannot repeat. This is a permutation problem where we arrange selected digits. The number of n-digit numbers with distinct digits (and first digit ≠ 0) is 9 × P(9, n-1) for n ≤ 10.
What You'll Learn
Introduction to Number Formation with Distinct Digits
Number Formation with Distinct Digits involves forming numbers where digits cannot repeat. This is a permutation problem where we arrange selected digits. The number of n-digit numbers with distinct digits (and first digit ≠ 0) is 9 × P(9, n-1) for n ≤ 10.
Prerequisites
How to Solve Number Formation with Distinct Digits Problems
Step 1: Identify the number of digits in the number (n)
Step 2: Recognize that digits cannot repeat (distinct digits)
Step 3: First digit cannot be 0: 9 choices (1-9)
Step 4: Remaining (n-1) positions: select from remaining 9 digits and arrange
Step 5: Use permutation: P(9, n-1) = 9!/(9-(n-1))!
Step 6: Total = 9 × P(9, n-1)
Step 7: For n = 1, numbers are 1-9 (9 numbers)
Example Problem
Example: How many 4-digit numbers can be formed using distinct digits? Solution: Step 1: n = 4 Step 2: First digit: 9 choices (1-9) Step 3: Remaining 3 digits: choose and arrange from remaining 9 digits Step 4: P(9,3) = 9 × 8 × 7 = 504 Step 5: Total = 9 × 504 = 4536 Answer: 4536 numbers
Pro Tips & Tricks
- n-digit distinct digit numbers: 9 × P(9, n-1)
- For n = 10: only one 10-digit number with all distinct digits (0-9), but first digit can't be 0, so 9 × 9!
- For numbers with leading zeros allowed: P(10, n)
- For n > 10: impossible (only 10 digits total)
- For n = 1: 9 numbers (1-9)
- For n = 2: 9 × 9 = 81 (first digit 1-9, second digit 0-9 except first)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Number Formation with Distinct Digits. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Number Formation with Distinct Digits is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Number Formation with Distinct Digits?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: