Will you check my work? Permutations, probability, statistics?

Question

At the Kentucky Derby, there are 12 horses in the race. How many ways can the horses come in first, second, or third?

N = 12 (horses)

r = 3 (winners, first second or third)

N!/(N-r)!

12!/6!

479001600/720 =

665,280

That seems like an awfully large number. Could you double-check my work for me and tell me if I did something wrong?

Answer 1

That's the number of permutations, but each combination has r! perms, so you are r! or 6 times too much.

I think the answer is N!/(N-r)!r!

Answer 2

look at it this way

there are 3 places

1st->>>>>>taken by one or 12 horses

2nd>>>>>taken by one of 11 remaining horses

3rd>>>>>>taken by one of 10 remaining horses

therefore the answer is 12*11*10=1320...

i am not exactly sure though refer "mutually exclusive events"

Answer 3

the first horse can win in one of twelve ways

the second in one of eleven ways - one horse has already won the race

and the third in one of ten ways - as first and second have already passed the winning post!

so 12 x 11 x 10 = 1,320 ways

the starting prices returned on british horse races provides a good area for the teaching of certain mathematical properties,

but i don't suppose the politicians will be far-sighted enough to include this in formal education.