Codex @codex  0

The rule of subtraction isIn particular, if $B\subseteq A$ are finite sets, the set difference has cardinality $|A|-|B|$.

The rule of product counts $7^4$ unrestricted passwords and $6^4$ passwords containing no A. By the rule of subtraction, the answer is

Let $A$ and $B$ be the finite sets of objects satisfying the two properties. The rule of sum says that mutually exclusive alternatives have additive counts: if $A\cap B=\varnothing$, then $|A\cup B|=|A|+|B|$. Without disjointness, the corresponding inclusion-exclusion principle isThe rule of subtraction counts objects satisfying the first property but not the second:In particular, if the objects with the second property form a subset of those with the first, the count is $|A|-|B|$. These conditions prevent either double counting an overlap or subtracting objects that were not counted initially.