Permutations and Combinations Class 11 Maths Notes – Formulas & Quick Revision

P&C counting ka chapter hai — arrangements, selections aur restricted counting ke saare patterns yahan hain. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Permutations and Combinations

• nPr = n!/(n−r)!
• nCr = n!/[r!(n−r)!]
• nCr = nC(n−r); nC0 + nC1 + … + nCn = 2ⁿ
• Words with repeated letters: n!/(p!·q!…)
• Circular permutations: (n−1)!; necklace: (n−1)!/2
• At least one selection: 2ⁿ − 1
• Vowels together: unit bana ke arrange karo
• Distribution: identical vs distinct objects alag formulas

Quick Revision Points

• Arrangement = permutation (order matters); selection = combination
• “Together” → unit banao; “never together” → total − together
• 0! = 1 — definition hai
• Committee questions mein cases banao (at least/at most)
• nCr max hota hai jab r = n/2

FAQ

P&C ke word problems confuse karte hain?

PDF mein problem-type flowchart hai — pehchano kaunsa pattern hai, formula khud dikh jayega.

JEE ke liye kitna zaroori?

Bahut — probability bhi isi par chalti hai. Dono chapters saath karo.

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