What is the Correct Equation for Pn and Qn in Permutation and Combination?

[nik jain]

Homework Statement

Let Pn denotes the no. of ways of selecting 3 people out of 'n' sitting in a row if no two of them are
consecutive and Qn is the corresponding figure when they are in circle .
If Pn - Qn = 6 , then 'n' is equal to:

The Attempt at a Solution

Pn = (n-2) C 3
Qn = (n-3) C 3
But I am getting wrong answer.
Please tell which one is wrong Pn or Qn .

 

[tiny-tim]

hi nik jain!

(try using the X² and X₂ buttons just above the Reply box )

Pn = (n-2) C 3
Qn = (n-3) C 3

i'm mystified …

why do you think that either of these is correct?

but anyway you don't need to find P_n or Q_n, you only need the difference …

what selections are in P_n but not in Q_n ? ​