different between perplexity vs derangement

English

perplex +? -ity, from Middle French perplexité or post-classical Latin perplexitas ‘entanglement’, from perplexus.

perplexity (countable and uncountable, plural perplexities)

The state or quality of being perplexed; puzzled or confused.
Something that perplexes.
- 1942, Rebecca West, Black Lamb and Grey Falcon (Canongate 2006), page 149:
  The Emperor, who was by then a focus of unresolvable perplexities, stood providing a strongly contrary appearance.
In information theory, a measurement of how well a probability distribution or model predicts a sample.

Borrowed from French dérangement.

derangement (countable and uncountable, plural derangements)

The property of being deranged.
An act or instance of deranging.
(mathematics, combinatorics) A permutation of a set such that no element is in its previous position.

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