Question 481474: pls help me solve this problem in probability... thank you..
a ring of keys can hold 7 keys. In how many ways can the keys be arranged if the ring can be turned over?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ring of keys can hold 7 keys.
the keys are a,b,c,d,e,f,g
the possible number of arrangements would be 7! = 7*6*5*4*3*2*1 = 5040.
let's see what happens if there are only 3 keys.
the number of arrangements would be 3! = 3*2 = 6
those arrangements would be:
a,b,c
a,c,b
b,a,c
b,c,a
c,a,b
c,b,a
if you turn the ring over, then:
a,b,c becomes c,b,a
a,c,b becomes b,c,a
b,a,c becomes c,a,b
b,c,a becomes a,c,b
c,a,b becomes b,a,c
c,b,a becomes a,b,c
since all these arrangements are already accounted for, there are no new arrangements that are created by flipping the ring over.
i would say that you get the same number of ways the keys can be arranged whether or not the ring can be turned over.
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