In a local dog show, there are prizes for first, second, and third place. If there are 11 dogs competing, how many ways are there to award the prizes (assuming no dog can win two prizes)?

Question

In a local dog show, there are prizes for first, second, and third place.  If there are 11 dogs competing, how many ways are there to award the prizes (assuming no dog can win two prizes)?

anonymous · Answer

The answer is 990 but I dont know how they got that.

anonymous · Answer

There are 11 dogs. There's only one possible dog for first place, and there are 11 possibilities. So you start with 11.

11

Now you have 2nd place. There are now 10 possibilities for 2nd place. Now...

11*10

Lastly, there is 3rd place. There are 9 possibilities for 3rd place. So...

11*10*9.

That is how they got 990.

anonymous · Answer

o ok. i think i was over thinking it. 
THANKS! :)

anonymous · Answer

Can you help with this question as well?

Commercial radio station call signs (i.e. WZZQ) are assigned following certain rules.  The first letter must be either "W" or "K" and the last three letters can be anything as long as they aren't all the same.  How many possible radio station call signs are possible?

How many different radio station call signs can you have with the first letter K and the second letter different from Q?

anonymous · Answer

Same as before. You can only start with one letter.

1

And the 4 following can be any letter, but can't be the same. So,

1*26*25*24

Does this make sense?