Question Detail
Question
What is the value of n, if P(15, n - 1) : P(16, n - 2) = 3 : 4?
Correct Answer
Option C is the correct answer.
Detailed Explanation
Given P(15, n - 1) : P(16, n - 2) = 3 : 4. Using the formula P(n, r) = n! / (n-r)!:[15! / (15 - (n-1))!] / [16! / (16 - (n-2))!] = 3/4[15! / (16-n)!] × [(18-n)! / 16!] = 3/4[15! / (16-n)!] × [(18-n)(17-n)(16-n)! / (16 × 15!)] = 3/4(18-n)(17-n) / 16 = 3/4(18-n)(17-n) = (3/4) × 16(18-n)(17-n) = 12We need to find two consecutive integers whose product is 12. These are 4 and 3.So, 18 - n = 4 (and 17 - n = 3).n = 18 - 4 = 14. Therefore, n = 14.
Hint
Write out the permutation formula for P(n,r) and simplify the ratio. Look for consecutive integers.