Check sibling questions

Ex 7.3, 7 - Find r if (i) 5Pr = 2 6Pr-1 (ii) 5Pr=6Pr-1 - Ex 7.3

Ex 7.3,7 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Ex 7.3,7 - Chapter 7 Class 11 Permutations and Combinations - Part 3 Ex 7.3,7 - Chapter 7 Class 11 Permutations and Combinations - Part 4

 

 


Transcript

Ex 7.3, 7 Find r if 5Pr = 2 6Pr – 1 Calculating 5Pr & 6Pr – 1 Given, 5Pr = 26Pr-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)! = 2 × 6!/(7 − 𝑟)! ((7 − 𝑟)! )/(5 − 𝑟)! = 2 × 6!/5! ((7 − 𝑟)(6 − 𝑟)(5 − 𝑟)! )/(5 − 𝑟)! = 2 × 6!/5! (7 – r)(6 – r) = 2 × 6!/5! (7 – r)(6 – r) = 2 × (6 × 5!)/5! (7 – r)(6 – r) = 2 × 6 (7 – r)(6 – r) = 12 7(6 – r) – r(6 – r) = 12 42 – 7r – 6r + r2 = 12 r2 – 13r + 42 – 12 = 0 r2 – 13r + 30 = 0 r2 – 3r – 10r + 30 = 0 r (r – 3) – 10 (r – 3) = 0 (r – 3) (r – 10) = 0 Hence, r = 3, 10 But, r < n So, r < 5 and r < 6 ∴ r = 10 is not possible So, r = 3 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.