Answer:
[tex]\frac{(n -1)!}{2}[/tex]
Step-by-step explanation:
Let us consider n beads of different colors, arranged in a line. If the beads were to be arranged in a straight line, there are n! ways to do this.
Now, if the beads were to be in a circular arrangement, a pattern will repeat n times.
So the number of different circular arrangements can be obtained by dividing by n, such that we get [tex]\frac{n!}{n}[/tex] = [tex](n-1)![/tex]
The patterns can be obtained via rotating either clockwise or anticlockwise, therefore 2 ways. So we can divide the total by 2.
Hence, the different number of necklaces which we can make from n beads of different colors is [tex]\frac{(n -1)!}{2}[/tex]
