In how many ways can 8 beads of different col | vedclass

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(A) The number of circular arrangements of $n$ distinct objects is $(n - 1)!$. For a necklace,the clockwise and counter-clockwise arrangements are con

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

(A) The number of circular arrangements of $n$ distinct objects is $(n - 1)!$. For a necklace,the clockwise and counter-clockwise arrangements are considered identical because the necklace can be flipped over. Therefore,the number of ways to arrange $n$ beads in a necklace is given by $\frac{(n - 1)!}{2}$. For $n = 8$,the number of ways is $\frac{(8 - 1)!}{2} = \frac{7!}{2}$. Calculating $7! = 5040$,we get $\frac{5040}{2} = 2520$.

In how many ways can $8$ beads of different colors be strung into a necklace?

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