Question Detail
Question
If n-1P3 : nP4 = 1 : 9, then what is the value of n?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The formula for permutations is nPr = n! / (n-r)!. Given n-1P3 : nP4 = 1 : 9.( (n-1)! / (n-1-3)! ) / ( n! / (n-4)! ) = 1/9( (n-1)! / (n-4)! ) * ( (n-4)! / n! ) = 1/9(n-1)! / n! = 1/9We know that n! = n * (n-1)!, so (n-1)! / (n * (n-1)!) = 1/9.1/n = 1/9Therefore, n = 9.
Hint
Write out the permutation formulas for n-1P3 and nP4 and simplify the ratio. Remember that n! = n * (n-1)!.