Ex 6.3, 7 - Find r if  (ii) 5Pr =  6Pr – 1 - Permutations - Teachoo - Ex 6.3

part 2 - Ex 6.3, 7 (ii) - Ex 6.3 - Serial order wise - Chapter 6 Class 11 Permutations and Combinations
part 3 - Ex 6.3, 7 (ii) - Ex 6.3 - Serial order wise - Chapter 6 Class 11 Permutations and Combinations

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Ex 6.3, 7 Find r if (ii) 5Pr = 6Pr – 1 Calculating 5Pr & 6Pr – 1 Given 5Pr = 6Pr – 1 5Pr = 5!/(5 − 𝑟)! 6Pr – 1 = 6!/(6 − (𝑟 − 1))! = 6!/(6 − 𝑟 + 1)! = 6!/(7 − 𝑟)! nPr = ((𝑛)!)/(𝑛 − 𝑟)! 5!/(5 − 𝑟)! = 6!/(7 − 𝑟)! ((7 − 𝑟)! )/(5 − 𝑟)! = 6!/5! ((7 − 𝑟)(6 − 𝑟)(5 − 𝑟)! )/(5 − 𝑟)! = 6!/5! (7 – r)(6 – r) = 6!/5! (7 – r)(6 – r) = (6 × 5!)/5! (7 – r)(6 – r) = 6 7(6 – r) – r(6 – r) = 6 42 – 7r – 6r + r2 = 6 r2 – 13r + 42 – 6 = 0 r2 – 13r + 36 = 0 r2 – 9r – 4r + 36 = 0 r (r – 9) – 4 (r – 9) = 0 (r – 4) (r – 9) = 0 Hence r = 4, 9 But, r < n So, r < 5 and r < 6 ∴ r = 9 is not possible So, r = 4 is the answer

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo