The number of ways that 8 beads of different | vedclass

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Question

(A) The number of ways to arrange $n$ distinct objects in a circle is $(n - 1)!$.For $8$ different beads,the number of circular arrangements is $(8 -

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

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

The number of ways that $8$ beads of different colours can be strung as a necklace is:

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