A car dealer lines up hist best objects during a sale She ha

A car dealer lines up hist best objects during a sale. She has m Porsche and n Ferrari. Supposing that m+n is even, how many antisymmetric ways to arrange the cars are there?

(Antisymmetric means that if the k-th car from the left is a Porsche then the k-th car from the right is a Ferrari.

I am having trouble visualizing how to figure out this problem. I believe that either both m and n are even or both m and n are odd is part of the answer.

Solution

your belief is correct.

m + n is even means either both should be even or both should be odd.

But m even and n odd or vice versa not possible.

If both are equal that means m is equal to n then there will be k=m=n anti symmetry lines.

similar would be for m = 3n=3 for odd

now if m and n are not equal then the number of symmetry lines will be equal to minimum of m or n.