Answer
75 ways
Work Step by Step
When there are no ties ,
number of ways = 4! = 24
When there is a tie between two horses
number of ways = $C$(4,2)×3! = 36
When there is a tie between 2 group of two horses
number of ways = $C$(4,2) = 6
When there is a tie between three horses
number of ways = $C$(4,3)×2! = 8
When there is a tie between all four horses
only 1 way in which this can happen
So total ways =24 + 36 + 6 + 8 + 1 = 75 ways
