First find the total number of ounces in the water cooler: 3 gallons * 128 ounces/gallon = <<3*128=384>>384 ounces
Then find the total number of dixie cups Bill pours: 5 rows * 10 chairs/row = <<5*10=50>>50 chairs
Then find the total number ounces Bill pours: 50 attendees * 6 ounces/attendee = <<50*6=300>>300 ounces
Then subtract the amount of water Bill pours from the cooler from the initial amount to find the final amount: 384 ounces - 300 ounces = <<384-300=84>>84 ounces
#### 84