#1

 A group of nine judges listen to arguments and independently respond in one of three ways:

Agree,  Disagree,   No Judgment

The judges report their responses to an argument as an aggregate response such as 5-3-1 (5 agree, 3 disagree, 1 no judgment) and 0-9-0 (0 agree, 9 disagree, 0 no judgment). The aggregate response is always in the order agree, disagree, no judgment.

 How many ways can the group of judges report their aggregate response to an argument?

#2

  Last year's judicial summary indicated that in no matter brought before the nine judges were there less than two judges who responded with "agree." The summary also stated that there was at least one "disagree" response to any argument. Given this information, how many ways existed for the group of judges to report their aggregate response to an argument?

#3

    Jeremy has a six-sided die. One side is colored green, one side is colored blue, two sides are colored red, and two sides are colored white. He rolls the die 100 times, each time recording the color that shows face up. After 100 rolls, Jeremy tell you how many of each color showed up. He begin by saying that 22 rolls were green. How many ways are there for Jeremy to finish his report? Please record responses on separate paper. Use a new sheet for each question. use one side only of each sheet of paper.