7 people, A, B, C, D, E, F and H, go to a movie and sit next to each

RupamPaul13
see highlighted part , but we have 8 seats to make 7 such options sit ; so wont it be 8P7 ways...

Sorry my bad, it should be 2* 7P6 as AF is taken as a single entity and they will occupy 2 seats. So 6 entity in 7 entities (seats) and AF can be arranged in 2 ways so 7P6

Total arrangements - Arrangements where A and F are together
Total - 8 Seats and 7 people = 8P7 = 720*7*8 = 4320
Arrangements where A and F are together = 7 seats and 6 people = 7P6*2 (As A and F can interchange) = 720*7*2 = 1080.
So 30240 arrangements Option D

Arvind42 why have you mentioned 7 seats and 6 people where as it should be 8 seats and 6 people...

Archit3110 But won't A and F require 2 seats to sit. So i reduced 1 from both the seats and people.

Arvind42
when taking case of A&F together cant we take in 8P6 ways ?

Archit3110. I don't think so. Cause we join A and F together for computational purposes (still we multiply the end result by 2 as we recognize that they can interchange between themselves). So the seat count should also be reduced to that extent.

Arvind42
OK i understood ...

Hi Archit3110

You have negated the possibilities where A and F are sitting together but will this still not include the cases where there is an empty seat in between A and F? Whereas the question mentions there must be a person between A and F.

Please explain

Posted from my mobile device

But there can be an empty seat b/w A and F in certain cases instead of a person.

How do we incorporate that into our solution ?

Bunuel chetan2u VeritasKarishma

I have the same query as quoted. Can you please provide an explanation?

Posted from my mobile device

The question is flawed, in both wording and answer..

Wording.. 7 people, A, B, C, D, E, F and H, go to a movie and sit next to each other in 8 adjacent seats in the front row of the theatre.
This means all are seating next to each other, so you can have V,_,_,_,_,_,_,_ or _,_,_,_,_,_,_,V ------- so 7!*2

But ofcourse question means
7 people, A, B, C, D, E, F and H, go to a movie and sit on 8 adjacent seats in the front row of the theatre.

Now, when this is what the question means..
at least one person between A and F implies even when there is a seat empty has to be subtracted ---- so we have to subtract (A,_,F) and 5 seats so 6!*2 from the final answer
Thus answer becomes 8!-7!*2-6!*2

But if the question was supposed to have answer as 8!-7*2!, then wordings should have been
at least one person chair between A and F

This question is a part of a series of examples in one of my blog posts to explain arrangements under constraints. There are no options given and it is not a standalone question. Hence, I have not given a lot of thought to the exact wording as long as the intent of the question is clear as in how it is different from the previous.
Request you to check out the entire post to get the context and the solution in detail: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/1 ... ts-part-i/

The intent of the question is that 7 people need to sit on 8 seats in the front row. In the solution, you do have to incorporate that there might be an empty seat between A and F and the answer given is 8! – 2*7! – 2*6! (which is not in the options - 28,800)