The number of members each state is eligible to send to the united states house of representatives

 That number is determined in proportion to each state's population, as reported by the US Census.

Detail:

There are 435 members  in the House of Representatives in Congress.  That number has been set at that level since 1929.  The number of representatives per state is adjusted after each census, which is conducted every 10 years.  The US Constitution (Article 1, Section 2), says:  "Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union."

Additional detail:

The number of electoral votes each state has in the Electoral College (for presidential elections) is also determined by the federal census.  Electoral College votes are aligned with the size of a state's overall Congressional representation, so the number of electoral votes each state gets (of the 538 total electoral votes) is recalculated every ten years, based on the most recent US Census data.

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~courtney