Question Detail
Question
If n-1P3 : nP4 = 1 : 9, then what is the value of n?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Given the ratio (n-1)P3 / nP4 = 1/9.Using the formula kPr = k! / (k-r)!:(n-1)P3 = (n-1)! / ((n-1)-3)! = (n-1)! / (n-4)!nP4 = n! / (n-4)!So, the ratio becomes: [(n-1)! / (n-4)!] / [n! / (n-4)!] = 1/9(n-1)! / n! = 1/9Since n! = n * (n-1)!,(n-1)! / [n * (n-1)!] = 1/91/n = 1/9Therefore, n = 9.
Hint
Express permutations using factorials and simplify the ratio. Remember n! = n * (n-1)!.