Question

in how many different ways four horses can cross the finish line

Answer 1

16 diffrent ways
hope it helps

Answer 2

The answer is 24, Here is why,

We know the concept of Permutations, I am going to apply it here,

Let the Horses be a,b,c,d, 
We know that, Either a can come in first place or the other, and this is similar for every other place,

We know that, If a comes in first place, then a can't come in second, third, and fourth place !

Which means, There is no repetition,

So now, according to this data,
Possible horses for first place = 4,
Possible horses for second place =3,[Since 1 horse will come 1st],
Possible horses for third place = 2,[Since another horse takes 2nd place],
Possible horses for fourth place = 1,[Since another horse takes 3rd place],

Now applying the Permutations,
=> No. Of Possible ways for horses to cross the finish line = 4*3*2*1 = 24,

Therefore the answer to your question is 24 different ways, For a Better understanding, Here are 2 different ways : (a,b,c,d) and (a,b,d,c)

Therefore the answer is 24,

Hope you understand, Have a Great Day ! Merry Christmas !
Thanking you, Bunti 360 !