Find n if ⁿ ^– ¹P₃: ⁿP₄= 1 : 9.

Solution:

Given that, ^{n – 1}P₃ : ⁿP₄= 1 : 9

^{n – 1}P₃ /  ⁿP₄= 1 / 9

Cross multiplying,

9 × ^{n – 1}P₃ = 1×ⁿP₄

Using nPr formula,

9(n - 1)!/[(n - 1) - 3]! = n!/(n - 4)!

9(n - 1)!/(n - 4)! = n!/(n - 4)!

9(n - 1)! = n(n - 1)!

9 = n

Thus, n = 9

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 6

Find n if ⁿ – ¹P₃ : ⁿP₄= 1 : 9.

Summary:

If ⁿ ^– ¹P₃: ⁿP₄= 1 : 9, then n = 9.