Odds of specific outcome when drawing names

Question

I'm desperate to have someone confirm (and explain) to me the right answer to the following!

The following are the specific circumstances for which I would like to know the odds of a certain occurrence:

There are 2 teams, each made up of 8 individuals. One team is captained by James and the Other team is captained by Tom. The members of each of the teams are separated into 2 separate hats in order to draw each player against a member of the opposition, i.e. 2 hats, each of which has 8 player names within. Names are drawn to create matches where members of the opposition teams play against each other (there will be 8 1 vs 1 matches).

What are the odds of Tom and James ending up being drawn to play against each other? The order is not a consideration, i.e. it doesn't matter whether they are drawn as the 1st or 2nd pair etc.

All players have to be pulled out of the hat at some stage of the draw.

Thanks.

Answer 1

HINT

Think of fixing the order of the players in the 1st hat, and then drawing the 2nd to match those. Since order of drawing is not important, the 1st hat's ordering makes no difference.

Now Tom can end up on any of the 8 resulting slots. What is the chance he will end up on the one corresponding to James?

Answer 2

The probability of Tom and James being drawn to play one another is $\frac 1 8$.

Think of it this way, there are 8 equally likely opponents for Tom, and James is one of them. Hence, one out of eight.