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

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Ex 7.3, 7 Find r if 5Pr = 2 6Pr โ€“ 1 Calculating 5Pr & 6Pr โ€“ 1 Given 5Pr = 26Pr-1 5!/(5 โˆ’ ๐‘Ÿ)! = 2 ร— 6!/(7 โˆ’ ๐‘Ÿ)! ((7 โˆ’ ๐‘Ÿ)! )/(5 โˆ’ ๐‘Ÿ)! = 2 ร— 6!/5! ((7 โˆ’ ๐‘Ÿ)(6 โˆ’ ๐‘Ÿ)(5 โˆ’ ๐‘Ÿ)! )/(5 โˆ’ ๐‘Ÿ)! = 2 ร— 6!/5! (7 โ€“ r)(6 โ€“ r) = 2 ร— 6!/5! (7 โ€“ r)(6 โ€“ r) = 2 ร— (6 ร— 5!)/5! (7 โ€“ r)(6 โ€“ r) = 2 ร— 6 (7 โ€“ r)(6 โ€“ r) = 12 7(6 โ€“ r) โ€“ r(6 โ€“ r) = 12 42 โ€“ 7r โ€“ 6r + r2 = 12 r2 โ€“ 13r + 42 โ€“ 12 = 0 r2 โ€“ 13r + 30 = 0 r2 โ€“ 3r โ€“ 10r + 30 = 0 r (r โ€“ 3) โ€“ 10 (r โ€“ 3) = 0 (r โ€“ 3) (r โ€“ 10) = 0 Hence r = 3, 10 Ex 7.3, 7 Find r if (ii) 5Pr = 6Pr โ€“ 1 Calculating 5Pr & 6Pr โ€“ 1 Given 5Pr = 6Pr-1 5!/(5 โˆ’ ๐‘Ÿ)! = 6!/(7 โˆ’ ๐‘Ÿ)! ((7 โˆ’ ๐‘Ÿ)! )/(5 โˆ’ ๐‘Ÿ)! = 6!/5! ((7 โˆ’ ๐‘Ÿ)(6 โˆ’ ๐‘Ÿ)(5 โˆ’ ๐‘Ÿ)! )/(5 โˆ’ ๐‘Ÿ)! = 6!/5! (7 โ€“ r)(6 โ€“ r) = 6!/5! (7 โ€“ r)(6 โ€“ r) = (6 ร— 5!)/5! (7 โ€“ r)(6 โ€“ r) = 6 7(6 โ€“ r) โ€“ r(6 โ€“ r) = 6 42 โ€“ 7r โ€“ 6r + r2 = 6 r2 โ€“ 13r + 42 โ€“ 6 = 0 r2 โ€“ 13r + 36 = 0 r2 โ€“ 9r โ€“ 4r + 36 = 0 r (r โ€“ 9) โ€“ 4 (r โ€“ 9) = 0 (r โ€“ 4) (r โ€“ 9) = 0 Hence r = 4, 9

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