Permutation and Combination
Permutation and Combination Data Sufficiency problems test your ability to determine if given statements provide enough information to count arrangements, selections, or combinatorial possibilities. You must assess sufficiency using factorial formulas and combinatorial reasoning.
What You'll Learn
Introduction to Permutation and Combination
Permutation and Combination Data Sufficiency problems test your ability to determine if given statements provide enough information to count arrangements, selections, or combinatorial possibilities. You must assess sufficiency using factorial formulas and combinatorial reasoning.
Prerequisites
How to Solve Permutation and Combination Problems
Step 1: Identify what is being asked (number of arrangements, selections, etc.)
Step 2: Translate each statement into counting conditions
Step 3: Check if Statement (1) alone gives a unique answer
Step 4: Check if Statement (2) alone gives a unique answer
Step 5: Combine statements if needed
Step 6: Remember that n must be known to calculate nPr or nCr
Step 7: Select the appropriate DS answer choice
Example Problem
Example: In how many ways can the letters of the word be arranged? Statement (1): The word has 5 distinct letters. Statement (2): The word has 2 vowels and 3 consonants. Solution: Step 1: Question asks for number of arrangements Step 2: Statement (1): 5 distinct letters → 5! = 120 ways → SUFFICIENT alone Step 3: Statement (2): 2 vowels and 3 consonants, but letters may not be distinct → need to know if letters are distinct or repeated → NOT sufficient alone Answer: Statement (1) alone is sufficient
Pro Tips & Tricks
- Number of permutations of n distinct items = n!
- Number of permutations with repetition = n!/(a!b!...) where a,b are repetition counts
- Number of combinations of n items taken r at a time = nCr
- To find nCr, need n and r
- Arrangements with restrictions need additional information
- Circular permutations = (n-1)!
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Permutation and Combination. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Permutation and Combination is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Permutation and Combination?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: