n! = A × n × (n-1) × (n-2) × ... × 2 × 1
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|
Call this A
= A × (n-1) × (n-2) × ... × 2 × 1
---------
|
Call this A
= A × (n-2) × ... × 2 × 1
.
.
= A × 1
= A
At each step, we made use of the fact that
A × B! = (A × B) × (B-1)!So at the end, A = n!