Question

In a 7 horse race, Bill thinks horses 1, 4, 6, will be the top 3 horses in the race, but not necessarily in that order. If Bill is correct, how many different outcomes are possible?

Answer 1

`3xx2xx1 = 6`

Explanation:

It is possible to work out the total number of outcomes that are possible without writing them all out and without using any formulae.

There are 3 different horses which can come first.
There are then 2 different horses which can come second.
There is one horse left to come third.

The number of possible arrangements is therefore:

`3xx2xx1 = 6` This is known as `3!` - called 3 factorial

If there were 4 horses, then the number of different possible outcomes would be `4xx3xx2xx1 = 24` This is known as `4!` - called 4 factorial