Permutation Question: How to Represent All 32 Possible System States

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A system that runs successfully needs 5 components to function properly. Each component is either operable (o) or inoperable (i). Thus the sequence OOOOi denots a state in which all components except the last component are operable.

How many states are possible?

I know the answer is 2^5 = 32, but how would I represent this as a permutation. Thanks.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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