$ x + 3 \equiv 0 \pmod{7} $, $ \pmod{8} $ → $ x \equiv -3 \pmod{7} $, $ \pmod{8} $
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\(2+1+1+1\)
\(1+1+1+1+1\)
Since the zones are indistinguishable, each unique distribution of turbine models corresponds to a partition of 5. We list the valid partitions for \( n = 5 \) with up to 4 parts:
\(5\) → one zone has all 5 turbines
\(4+1\) → one zone has 4, another has 1
\(3+2\) → one zone has 3, another has 2
\(3+1+1\) → one zone has 3, two have 1 each
\(2+2+1\) → two zones have 2 each, one has 1
\(2+1+1+1\) → one zone has 2, three have 1 each
Each of these partitions corresponds to a distinct way to assign the turbine models to indistinct zones, because the zones cannot be distinguished and only the frequency of turbine counts matters.