There are 10 students running a race. The fastest three get a gold, silver, or bronze medal. How many different ways can the students win these medals?

Question

There are 10 students running a race.  The fastest three get a gold, silver, or bronze medal.  How many different ways can the students win these medals?

anonymous · Answer

I know it's more than 30, but I'm not sure what to multiply after that!  Help!

amistre64 · Answer

10 ways to come in 1st; leaves 9 left
9 ways to come in 2nd; leaves 8 left
8 ways to come in 3rd

amistre64 · Answer

10.9.8

anonymous · Answer

is this the formula with the ! in it?

amistre64 · Answer

its one of them:

  10!
------
(10-3)!

anonymous · Answer

Or if your calculator has the nPr function, you can type in 10nPr3 to get the same answer.

amistre64 · Answer

which is just 10 pick 3

anonymous · Answer

Thanks!  I have another ready to go on the other side!  I like to know if I'm doing these correctly!

anonymous · Answer

10c3 =10*9*8 = 720

anonymous · Answer

10 nPr 3 =720