Final answer:
The Battle of Austerlitz was between France and the allied forces of Austria and Russia, with France having around 68,000 troops and the opponents about 90,000 troops. France's decisive victory led to Austria seeking an armistice and Russia's retreat.
Step-by-step explanation:
The Battle of Austerlitz
The Battle of Austerlitz, also known as the Battle of the Three Emperors, was a decisive military engagement fought between the armies of France under Napoleon Bonaparte and a combined force of the Austrian Empire and Russia. The battle took place on December 2, 1805, and is heralded as one of Napoleon's greatest victories. Option b in the multiple-choice question provided correctly states that France had approximately 68,000 troops, while the allied forces of Austria and Russia had around 90,000 troops.
The engagement ended with a strategic victory for France, leading Austria to seek an armistice and compelling Russia to retreat back into Eastern Europe. Following this victory, Napoleon further solidified his power by arranging a marriage with Marie-Louise of Austria, establishing a political alliance after his military triumph.