Permutation and Combination
About 5 min · Numerical Ability · English
Time worked out from the lesson's 285 words at 150 words a minute, plus a minute for each question.
Permutation and Combination forms the foundation of counting problems in competitive exams.
Key ideas
- Fundamental Counting Principle: If task A can be done in 'm' ways and task B in 'n' ways, both tasks together can be done in m × n ways (for AND) or m + n ways (for OR).
- Factorial (n!): Product of all positive integers from 1 to n. Example: 5! = 5 × 4 × 3 × 2 × 1 = 120. Special case: 0! = 1.
- Permutation (nPr): Number of ways to arrange 'r' items from 'n' distinct items. Order matters—ABC is different from BAC.
- Combination (nCr): Number of ways to select 'r' items from 'n' distinct items. Order doesn't matter—selecting A, B, C is same as selecting B, C, A.
- Key relationship: nPr = nCr × r! (Every combination can be arranged in r! ways to get permutations).
Quick reference
- Order matters → Permutation (nPr); Order doesn't matter → Combination (nCr)
- nPr = n!/(n-r)! and nCr = n!/[r!(n-r)!]
- Repeated letters: Divide n! by factorial of each repetition count
- nCr = nC(n-r) — use smaller value for faster calculation
- At least one = Total − None
Check yourself: 3 questions
1. In how many different ways can the letters of the word 'ORANGE' be arranged so that the vowels always come together?
2. A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can this be done if the committee must contain at least 2 women?
3. A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can this be done if the committee must contain at least 2 women?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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