The number of ways in which 5 beads of differ | vedclass

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Question

(A) The number of ways in which $n$ distinct beads can be arranged in a circle is $(n - 1)!$.For a necklace,the clockwise and anticlockwise arrangemen

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) The number of ways in which $n$ distinct beads can be arranged in a circle is $(n - 1)!$.For a necklace,the clockwise and anticlockwise arrangements are considered identical because the necklace can be flipped over.Therefore,the number of ways to form a necklace with $n$ beads is $\frac{(n - 1)!}{2}$.For $n = 5$,the number of ways is $\frac{(5 - 1)!}{2} = \frac{4!}{2} = \frac{24}{2} = 12$.

The number of ways in which $5$ beads of different colours form a necklace is

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