9.93 The toys manufactured by the factory are in the shape of a ring, with 3 red beads and 7 blue beads strung on it. How many different types of such toys can be manufactured? (If the arrangement of red and blue beads on the ring of two toys is the same or if one can be flipped over to match the arrangement of the other, they are considered the same type)


[Solution] 3 red beads divide 7 blue beads into 3 groups. Of course, one or two groups of blue beads may be zero. Therefore, the number of different ways sought is exactly equal to the number of different ways to divide 7 into the sum of 3 non-negative integers. The partitions of 7 are only the following 8: $7+0+0, 6+1+0, 5+2+0, 5+1+1, 4+3+0, 4+2+1, 3+3+1, 3+2+2$. Therefore, the factory can produce a total of 8 different toys.