Key Ring
Posted May 14, 2009
By admin
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How many arrangements are needed to show all permutations of 5 keys on a circular key ring?
this q is tricky as it depends on interpretation
i take it that the ring has a chain
which has the effect of numbering positions,
and that the chain has a "face"
which makes clockwise/anticlockwise relevant
under the above assumptions,
# of arrangements = 5! =120
if some of the conditions are different from what i hv assumed,
u shd easily be able to adjust the answer accordingly
edit:
------
might as well give ans under differing assumptions
(a) if the chain doesn't hv a "face",
i.e. flipping the ring changes clockwise orientation,
# of ways = 5!/2 = 60
(b) if there is no chain, just a ring,
so that positions are unidentifiable,
# of ways = 4!/2 = 12,
[divide by 2 since by flipping the ring,
clockwise/anticlockwise orientation can be changed]
NOTE:
---------
jordi's ans wd b correct
if the q was re sitting at a circular table
there the clockwise/anticlockwise orientation
can't be changed .
but if it is a key ring w/o chain [ assumption (b) ],
it becomes a different problem
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