Question
Mathematics Question on permutations and combinations
Find the value of n such that nP5=42nP3,n>4.
A
10
B
15
C
12
D
20
Answer
10
Explanation
Solution
We have nP5=42nP3 ⇒n(n−1)(n−2)(n−3)(n−4)=42n(n−1)(n−2) ⇒(n−3)(n−4)=42 [Since n>4, so n(n−1)(n−2)=0] ⇒n2−7n−30=0 ⇒n2−10n+3n−30=0 ⇒n=10 or n=−3 As n cannot be negative, so n=10