In how many ways can 5 keys be put in a ring? | vedclass

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(A) The number of ways to arrange $n$ distinct objects in a circle is $(n - 1)!$.However,for arrangements like keys in a ring or beads in a necklace,t

Vedclass · Accepted Answer

$\frac{1}{2}4!$

Vedclass · Answer

(A) The number of ways to arrange $n$ distinct objects in a circle is $(n - 1)!$.However,for arrangements like keys in a ring or beads in a necklace,the clockwise and anticlockwise arrangements are considered identical because the ring can be flipped over.Therefore,the formula for the number of ways to arrange $n$ keys in a ring is $\frac{(n - 1)!}{2}$.For $n = 5$ keys,the number of ways is $\frac{(5 - 1)!}{2} = \frac{4!}{2}$.

In how many ways can $5$ keys be put in a ring?

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