1). How many ways can 5 people sit in a circular arrangement?
2). If there are 6 distinct chairs arranged in a circle, in how many ways can 3 people sit such that no two people sit together?
3). In how many ways can 4 people sit around a circular table if two of them insist on sitting opposite to each other?
4). If you have 8 different flags and want to arrange them in a circular pattern, how many different arrangements are possible?
5). If there are 7 children standing in a circle, in how many ways can they be given identical balloons if no two adjacent children can have the same color?
6). How many different necklaces can be made using 5 distinct beads if rotating a necklace doesn't change its appearance?
7). A necklace has 10 beads of different colors. How many different ways can the necklace be arranged?
8). In a circular garden, there are 6 distinct trees. In how many ways can you arrange 3 of them such that no two are adjacent?
9). How many different ways can 8 people stand in a circle if two specific individuals refuse to stand next to each other?
10). In how many ways can you arrange 4 red, 3 green, and 2 blue balloons in a circular arrangement?
11). There are 9 different keys on a circular keyring. In how many ways can you arrange the keys such that 2 particular keys are always together?
12). How many distinct arrangements can be made with 5 red, 3 blue, and 2 green flags in a circular fashion?
13). If there are 10 students and 5 chairs in a circular arrangement, how many ways can they sit if 2 students refuse to sit next to each other?
14). In how many ways can 6 friends be seated around a circular table if 2 of them insist on sitting together?
15). How many different ways can you arrange 5 distinct flowers in a circular vase?
16). If you have 7 different candies and want to arrange them in a circular pattern, how many different arrangements are possible?
17). In a circular arrangement of 9 chairs, how many ways can 4 people sit such that no two people are adjacent?
18). How many distinct arrangements are possible with 8 identical coins placed on a circular table?
19). If there are 12 different books on a circular bookshelf, how many ways can you arrange 4 specific books such that they are not next to each other?
20). In how many ways can 10 people be seated in a circular arrangement if 3 specific people must always sit together?
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