Question:
The number of ways that 8 beads of different colours can be strung to form a necklace is
The number of ways that 8 beads of different colours can be strung to form a necklace is
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For a necklace of n distinct beads the count is (n-1)!/2.
Updated On: Oct 1, 2026
- \(5040\)
- \(2520\)
- \(2840\)
- \(5080\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Arranging \(n\) distinct objects in a circle gives \((n-1)!\) arrangements. For a necklace, flipping it over gives the same pattern, so each arrangement is counted twice.
Step 2: Apply the formula:
\[ \dfrac{(8-1)!}{2} = \dfrac{7!}{2} = \dfrac{5040}{2} = 2520 \]
Step 3: Why the other options are wrong.
5040 is the count of circular arrangements without turning the necklace over. 2840 and 5080 do not match either formula.
Final Answer:
There are 2520 ways. \[ \boxed{\text{(B) }2520} \]
Arranging \(n\) distinct objects in a circle gives \((n-1)!\) arrangements. For a necklace, flipping it over gives the same pattern, so each arrangement is counted twice.
Step 2: Apply the formula:
\[ \dfrac{(8-1)!}{2} = \dfrac{7!}{2} = \dfrac{5040}{2} = 2520 \]
Step 3: Why the other options are wrong.
5040 is the count of circular arrangements without turning the necklace over. 2840 and 5080 do not match either formula.
Final Answer:
There are 2520 ways. \[ \boxed{\text{(B) }2520} \]
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