Question Detail
Question
If nP4 : nP2 = 12, find the value of n.
Correct Answer
Option C is the correct answer.
Detailed Explanation
The formula for permutations is nPr = n! / (n-r)!. Given nP4 : nP2 = 12.(n! / (n-4)!) / (n! / (n-2)!) = 12(n! / (n-4)!) * ((n-2)! / n!) = 12(n-2)! / (n-4)! = 12(n-2) * (n-3) * (n-4)! / (n-4)! = 12(n-2) * (n-3) = 12n² - 5n + 6 = 12n² - 5n - 6 = 0Factoring the quadratic equation: (n-6)(n+1) = 0.Possible values for n are 6 and -1. Since n must be a positive integer (and at least 4 for nP4 to be defined), n = 6.
Hint
Use the definition of permutations nPr = n! / (n-r)! and simplify the ratio to form a quadratic equation.