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

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

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