Derived some identities while thinking on what James Randi said in the following video (James Randi and a Graphologist) after 1 minute 50 seconds.

Let d0 = 1 and dn be the number of derangements of n elements, where n is a positive integer.

nnC0d0 + (n − 1)nC1d1 + … + 0nCndn = n!

nC0d0 + nC1d1 + … + nCndn = n!

Update: A detailed blog here: James Randi and a graphologist

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