40. Suppose a necklace is made of n distinct beads without a clasp (this means y

Question

40. Suppose a necklace is made of n distinct beads without a clasp (this means you don't know the beginning or the end). Assume someone can pick up the necklace, move it around in space and put it back down, giving an apparently different way of stringing the beads that is equivalent to the first. (a) How can you get a list of beads from a necklace? (b) How many permutations of the beads are there? (C) Describe a way to partition the set of permutations of the beads into blocks that give equivalent necklaces. (d) Using your answers to parts (a) through (C), determine the number of distinct necklaces that can be made.

Explanation / Answer

For linear chain , the arrangment is in such a way that there are n! ways to do it .
In circular necklace, there are some arrangements which are same but are at different positons and due to symmetry of circle they shouldn't be considered
ways we string n distinct beads on a necklace without a clasp=(n-1)!

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.