Ex 6.3 Q9 Class 11 Maths Chapter 6 PnC | MONDAY Word Formation— (4-letter / 6-letter / Vowel-first)

Описание: In this video we solve all three parts of Question 9 Exercise 6.3 from Class 11 Maths NCERT Chapter 6 — Permutations & Combinations (PnC).

Question: From the letters of the word MONDAY (all distinct), how many words (with or without meaning) can be made, assuming no letter is repeated, if:
(i) 4 letters are used at a time, (ii) all letters are used, (iii) all used but first letter is a vowel?

🔢 Algorithm (step-by-step thinking — exam style)

Part (i) — 4 letters used at a time

Rule: Order matters → use permutation P(6,4).

Algorithm: choose sequentially: first place 6 choices → second 5 → third 4 → fourth 3 → multiply.

Part (ii) — all letters used

Rule: all letters distinct and all used → use factorial 6!.

Algorithm: arrange 6 distinct objects → multiply 6 × 5 × 4 × 3 × 2 × 1.

Part (iii) — all used but first letter a vowel

Identify vowels (O, A) → choose first letter (2 choices).

Arrange remaining 5 letters in remaining slots → 5! ways.

Algorithm: multiply choices for first letter × permutations of remaining positions.

🎯 Final Answers (quick)

(i) P(6,4)=6×5×4×3=360

(ii) 6!=720

(iii) 2×5!= 2×120=240


💡 Why watch this video (exam benefits)

Learn the decision rule: Order matters → permutation; all distinct & all used → factorial.

Practice the sequential-choice algorithm so you can compute quickly in board exams, JEE Main, and CUET.

Shortcuts and mental-multiplication tips to save time under pressure.

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