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Permutations & Combinations
· Examples✏️ Worked Examples — Step by Step
E1
EasyIn how many ways can the letters of the word "MATH" be arranged?
💡 All distinct letters, all positions used → n!
👁 Show Solution
4 distinct letters, all arranged: 4! = 4 × 3 × 2 × 1 = 24 ✅ Answer: 24
✅24
E2
MediumHow many ways can a committee of 3 be chosen from 7 people?
💡 Order doesn't matter → use nCr.
👁 Show Solution
7C3 = 7! / (3! × 4!) = (7 × 6 × 5) / (3 × 2 × 1) = 35 ✅ Answer: 35
✅35
E3
ChallengingHow many 4-digit numbers can be formed using digits 1–9 without repetition?
💡 Order matters → use nPr.
👁 Show Solution
9P4 = 9 × 8 × 7 × 6 = 3024 ✅ Answer: 3024
✅3024