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AMC / AIME · Inclusion-Exclusion · AIME / USAJMO / AMO

Inclusion-Exclusion: (Proof track.) Derive the derangement formula math and enter math.

Unions without double-counting.

Try the problem

**(Proof track.)** Derive the derangement formula !n=n!∑k=0n(−1)k/k!!n=n!\sum_{k=0}^{n}(-1)^k/k! and enter !7!7.

Hint and answer

Concept to use

Full PIE.

Hint

Standard value.

Answer

1854

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