Should I apply multiple companies for internship?

I will have my internship then graduate and look for job since finding an internship is hard task lately and I am 30 I am planning to apply all possible internships maybe around 200 companies in total but since I will only have one internship I will reject others will this effect their opinion on me if I apply for full time job later on. And am I being too optimistic thinking there will be multiple companies accepting me as a 30 years old new grad, maybe there will already be 1 or 2 companies accepting me or even zero? I am applying software developer jobs

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