A car dealer lines up his best objects for sale. He has 'n' Porsche and 'n' Ferrari. How many anti-symmetric ways are there to arrange these cars? (Anti-symmetric means that if ith from left is a Porsche then the ith from right must be a Ferrari and other way round).
My try:
I am relating it to Binomial expansion because first and last term are equal in it and so on.
According to me there should be 2 ways (one starting with Porsche and one starting with Ferrari)
There are $2^n$ ways (assuming all the Porsches are indistinguishable from each others, and Ferraris likewise). The first $n$ cars (from the left) can be arranged arbitrarily, the second $n$ cars (looking from right to left) are the same, but with every P replaced by F and vice versa.