14. Suppose there are 3 distinct green balls, 4 distinct red balls, and 5 distinct blue balls in an urn. The balls are to be grouped into pairs such that the balls in any pair have different colors. How many sets of six pairs can be formed?
Answer: 1440
Solution: Since there are 7 green and red balls combined, and 5 blue balls, then there should be one pair with 1 green and 1 red, and all the other pairs must have a blue ball. There are $3 \times 4$ ways of selecting a green-red pair, and 5! ways of selecting the partners for the blue balls. Thus, there are $3 \times 4 \times 5!=1440$ possible pairings.