Final answer:
The Empress Dowager allowed the Boxers to exist because she wanted to use them to expel foreign influences from China, aligning with her political objectives.
Step-by-step explanation:
The Empress Dowager Cixi permitted the existence of the Boxers because she believed they could help expel foreign influence from China. Option C) She wanted to use the Boxers to get rid of the foreigners is the correct answer. The Boxer Rebellion was a significant historical event where the Boxers, a nationalistic secret society in China, initiated an uprising with ambitions to eliminate all foreign forces and influences. Despite the risks, the Empress Dowager saw an opportunity in this ideology to end foreign dominance in China, which aligned with her own political objectives. As a result, instead of suppressing the Boxers, she supported their cause against the foreigners.