Probability Question (1 Viewer)

[kevinsta]

To win a trifecta in a race, a
person has to pick the horses
that come first, second and
third in the race. For a certain
race, Marie wishes to bet on
every combination possible to
win the trifecta. If there are 12
horses in the race, how many
combinations will she bet on?

PS: Stuck on this question please help me solve it.

 

[Queenroot]

too many

 

[Carrotsticks]

We need to first choose 3 horses from the 12, so its 12C3.

But because the order in which they win is important, we need to permute them, so 3!

So the answer is 3! x 12C3.

As an extension, we should also note that Marie is a very silly person for undergoing such a tactic.