Step 1: Understanding the Concept
Amines react with alkyl halides by nucleophilic substitution. With excess alkyl halide the reaction goes on until the nitrogen carries four groups (exhaustive alkylation).
Step 2: Detailed Explanation
\(\text{C}_2\text{H}_5\text{NH}_2 \to \text{C}_2\text{H}_5\text{NHCH}_3 \to \text{C}_2\text{H}_5\text{N(CH}_3)_2 \to [\text{C}_2\text{H}_5\text{N(CH}_3)_3]^+\text{I}^-\).
Each step adds one methyl group. After three methylations the nitrogen has the ethyl group and three methyl groups.
The final product is ethyltrimethylammonium iodide. The ethyl group stays, so tetramethylammonium iodide cannot form.
Final Answer:
The major product is ethyltrimethylammonium iodide, option (B).
\[ \boxed{\text{Ethyltrimethylammonium iodide (B)}} \]