1. ## Combinations/Permutations

Hi,

This will probably be very easy for most people on this site but i have no clue.

I am trying to work out how many combinations there are for ten events each with three possible outcomes.

Example:If you take 10 football matches each having three outcomes e.g home win,draw,away win, how many possible outcomes are there for all mathches and outcomes.

I was told it might be 10 to the power of 3 but not sure and dont know how to work that out anyway.

2. Originally Posted by redredneck
Hi,

This will probably be very easy for most people on this site but i have no clue.

I am trying to work out how many combinations there are for ten events each with three possible outcomes.

Example:If you take 10 football matches each having three outcomes e.g home win,draw,away win, how many possible outcomes are there for all mathches and outcomes.

I was told it might be 10 to the power of 3 but not sure and dont know how to work that out anyway.

$3^{10}$.

Make the pigeonhole principle your friend.

3. Hi,

Cheers for that but i dont know how to do this,could you please explain how i work out?

Thankyou

4. ## Perm/Comb

There are 3 outcomes for the first match.
3 outcomes for the second.
3 outcomes for the third.
.
.
.
3 outcomes for the tenth.

So, the number of possible outcomes = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = $3^{10}$.

I hope that makes it clear.

me07.