Ex 7.3,6 - Find n if  n-1P3 : nP4 = 1 : 9 - Chapter 7 - Permutation formula

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise

Transcript

Ex 7.3, 6 Find n if n โ€“ 1P3 : nP4 = 1 : 9. Lets first calculate n โ€“ 1P3 and nP4 separately n โ€“ 1P3 = ((๐‘›โˆ’1)!)/(๐‘›โˆ’1 โˆ’3)! = ((๐‘›โˆ’1)!)/(๐‘›โˆ’4)! = (๐‘› โˆ’ 1)(๐‘› โˆ’ 2)(๐‘› โˆ’ 3)(๐‘› โˆ’ 4)!/(๐‘›โˆ’4)! = (n โ€“ 1)(n โ€“ 2)(n โ€“ 3) It is given that n โ€“ 1P3 : nP4 = 1 : 9 "n โ€“ 1P3" /"n P4" = "1" /" 9" 9 (n โ€“ 1P3) = nP4 9(n โ€“ 1)(n โ€“ 2)(n โ€“ 3) = n(n โ€“ 1)(n โ€“ 2)(n โ€“ 3) 9"(n โ€“ 1)(n โ€“ 2)(n โ€“ 3)" /"(n โ€“ 1)(n โ€“ 2)(n โ€“ 3)" = n 9 = n n = 9

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