Q56 / 150 · MHT CET 2026 (11 April Shift 2) · Mathematics
The number of ways that 8 beads of different colours can be strung to form a necklace is
- A$5040$
- Correct answerB$2520$
- C$2840$
- D$5080$
Solution
The number of ways to arrange $n$ distinct objects in a circle is $(n-1)!$.
For a necklace, clockwise and counter-clockwise arrangements are considered identical because it can be flipped over.
Therefore, the number of ways to string $n$ different beads into a necklace is $\dfrac{(n-1)!}{2}$.
Given $n = 8$, the number of ways is $\dfrac{(8-1)!}{2} = \dfrac{7!}{2}$.
Since $7! = 5040$, the number of ways is $\dfrac{5040}{2} = 2520$.
Answer: $2520$
For a necklace, clockwise and counter-clockwise arrangements are considered identical because it can be flipped over.
Therefore, the number of ways to string $n$ different beads into a necklace is $\dfrac{(n-1)!}{2}$.
Given $n = 8$, the number of ways is $\dfrac{(8-1)!}{2} = \dfrac{7!}{2}$.
Since $7! = 5040$, the number of ways is $\dfrac{5040}{2} = 2520$.
Answer: $2520$
Hence, the correct answer is option: 'B'.