There are 7! = 5040 ways in which seven people can form a line. In how many ways can seven people form a circle
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Let us find the number of ways that seven people form a circle. Let us fix some position. For this position thare are 7 ways to seat a person. Let us move in the clockwise direction. For the next position thare are 6 ways to seat a person, and so on. For the last postion there is one way to seat a person. By Combinatirial Product Principle, the number of ways that seven people form a circle with fixed initial position on the circle is equal to Since each way with fixed position generates 7 different ways that form the same circle, the number of ways that seven people form a circle is equal to