Permutations And Combinations Question 242

Question: If $ {}^{n}P_5=20.\ {}^{n}P_3 $ , then $ n= $

Options:

A) 4

B) 8

C) 6

D) 7

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ \frac{n\ !}{(n-5)\ !}\times \frac{(n-3)\ !}{n\ !} $ =20  
    

$ \Rightarrow $ $ (n-3)(n-4)=20\Rightarrow n=-1,\ 8 $ But $ -1 $ is not exceptable.