Table Structure - Not Duplicating Records

Here's another one I'm stumped on. What would be the best way to do this... if it can be done:

The tables in question are the following:

1. Exhibitors (stores exhibitor data, i.e. name, age, address, etc)
2. Livestock (stores livestock data for each exhibitor, i.e. breed, weight, gender)
3. Shows (stores data about each show, i.e. title, date, location)

I would like to have the Shows table to also store which exhibitors and livestock participated at this show. For example:

County Show: Jane Doe (exhibitor) - blackie, whitie (livestock)
John Smith - spot, blue, cutie-pie
James Black - smokey, sassy, fluffy

State Show: Jane Doe - blackie
James Black - spot, blue, cutie-pie, snuffles
Christy Meek - baby, apples

The problem is that each show will be associated with multiple exhibitors (and their different livestock). AND each exhibitor (and their livestock) will be associated with different and often times multiple shows.

So what would be the best way to have the Shows table pull the exhibitor and livestock data without having to duplicate exhibitor records for each show?