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If 5 × 4Pr = 6 × 5Pr – 1, Then find the value of r.1. 42. 53. 34. 2 |
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Answer» Correct Answer - Option 3 : 3 Given: 5 × 4Pr = 6 × 5Pr – 1 Formula used: P (n, r) = n!/(n –r) ! Where, The number of possible arrangements for are objects from a set of n object. Calculation: 5 × 4Pr = 6 × 5Pr – 1 ⇒ 5 × [4!/(4 – r)!] = 6 × [5!/{5 – (r – 1)!}] ⇒ 5 × [4!/(4 – r)!] = (6 × 5 × 4!)/(6 – r)! ⇒ (5 × 1)/(4 – r)! = (6 × 5)/(6 – r) × (5 – r) × (4 – r)! ⇒ 1 = 6/(30 – 11r + r2) ⇒ r2 – 11r + 30 = 6 ⇒ r2 – 11r + 30 – 6 = 0 ⇒ r2 – 11r + 24 = 0 ⇒ r2 – 8r – 3r + 24 = 0 ⇒ r(r – 8) – 3(r – 3) = 0 ⇒ (r – 8) × (r – 3) = 0 If, (r – 8) = 0 ⇒ r = 8 Either, (r – 3) = 0 ⇒ r = 3 In expression n = 4 or 5 ⇒ n ≤ 5 ⇒ n ≠ 8 ⇒ n = 3 ∴ The value of r is 3. |
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