Perms and combs help (1 Viewer)

[mathsbrain]

Twelve people sit around two tables labelled A(5 seats) and B(7 seats), how many ways can this be done.

The solution says 12C5*4!*6! which i understand works.
I was thinking doing 1*11*10*9*8* 1*6*5*4*3*2*1 which gives a different answer.
My logic is, the first person that sits down on table A has only one option since all seats are the same to him.
Then 11 options for the person next to him, 10 , 9 and 8 to fill remaining spots.
Then we move to table B, again out of the 7 people left, the first person that sits down has only 1 option, then 6, 5,...1
Whats wrong with this?

 

[aa180]

I think your mistake is that you are forcing the first person to only sit at table A, and discounting all of the arrangements where he/she sits at table B. To follow your approach in full completion, you can consider when the first person starts off at table B, and count the corresponding arrangements which will be given by 11*10*9*8*7*6*4!, and upon adding this to your calculation, will then give the correct answer