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Out of this B and C will be adjacent 2*6!/2 times = 720

I believe the answer should be 2520-720 = 1800.

I doubt if it can be done so easily. Because "adjacent" means "close to", so, it can happen that A and B are adjacent, and there is no room for C between them. C is adjacent to A when AC or CA take place. Am I right?

I misread the question. The stem says horse C is not adjacent to either of them. Then no of arrangements = 3! * 5! out of this A ia ahead of B half the time
I believe it is time for halle to post the answer.

I misread the question. The stem says horse C is not adjacent to either of them. Then no of arrangements = 3! * 5! out of this A ia ahead of B half the time I believe it is time for halle to post the answer.

3! * 5! /2 = 360

Moreover, the answer should be such that = 24 mod 48. Because for every pattern of A,B,C there exists an inverse pattern, with only one exception of (*,*,A,C,B,*,*). Inverse = {change A & B in (*,*,B,C,A,*,*)}.

my guess
(7! -(2*5! + 2*5!))/2 = 2280
{C would never be adjacent to A * B in 4540 ways) and A would be ahead of B in half of them.
---trying to think simple here--
_________________

my guess (7! -(2*5! + 2*5!))/2 = 2280 {C would never be adjacent to A * B in 4540 ways) and A would be ahead of B in half of them. ---trying to think simple here--

Your answer looks like normal, since it has 24 mod 48... And is less than 2520.