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In how many ways can seven beads of different colours be threaded in a circular...

In how many ways can seven beads of different colours be threaded in a circular ring?

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Answers (2)

isaaq
1 week ago
For every ordering of 6 beads, of which there are 7!, you can rotate that arrangement 5 times to produce 7 orderings that all must be counted together. For example
abcde = bcdea = cdeab = … = eabcd (7 total)
Given that we count each arrangement 7times, there are a total of 7!/7= 360 ways to make distinct circular rings with 7 beads.
victory
1 week ago
using cyclic permutation
1 x(n-1)!
1 x(n-1)!/2
= 1 x(7-1)!/2
=6!/2
=720/2
=360 ways
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