probabilty - different orders of horses winning a race

[sniperkiller]

Hi, I'm trying to get this question right, and no matter how often I look back at past papers, it just doesn't make sense to me.

Seven horses run a race. All horses finish the race and no two horses finish the race at the same time.

(i)In how many different orders can the seven horses finish the race?

I think this is right: 7!, which is 7.6.5.4.3.2.1, 5040.

(ii)A person is asked to predict the correct order of the first 3 horses to finish the race. How many such predictions can be made?

Hmmm. Not sure of this.

(iii)A person is asked to predict, in any order, the first 3 horses to finish the race. How many such predictions can be made?

I think this is: 7!/(7-3)!, which is 7!/4!, = 210.

Anyway, I'd be grateful for any help,

Regards,

Chris.

 

[tkhunny]

Seven horses run a race. All horses finish the race and no two horses finish the race at the same time.

(i)In how many different orders can the seven horses finish the race?

I think this is right: 7!, which is 7.6.5.4.3.2.1, 5040.

Do you believe that to be incorrect?

Put letters on the horses, so we can tell them apart, ABCDEFG.

Are these the same order?
ABCDEFG
BCDEFGA
CDEFGAB
DEFGABC
EFGABCD
FGABCDE
GABCDEF

 

[sniperkiller]

Ok, 5040 is the number of possible orders. But what about part (ii) and (iii)?

I'm confused as to the difference between: the correct order of the first 3 horses, and the first 3 horses on any order.

Thanks.

 

[pka]

The difference is a simple as this.
The string ABC is different from the string CBA.
But the set {A,B,C} is the same as the set {C,B,A}
The strings represent the order of winning; the sets represents collection of winners.