If I apply to 10 undergraduate schools what're the odds I get into AT LEAST ONE?

[1NJParent]

Are my odds of gettIng a job the exact same if I apply to only 1 firm or if I apply to 10 firms?

I think we would all say that by applying to 10 firms will increase my odds (even if only slightly) of getting a job offer by at least one firm.

Yes, your odds of getting at least one offer are higher unless the 10 firms look at your applications in exactly the same way (i.e. the correlation between them is perfect or 1). In reality, since the correlation isn’t perfect, your chances are better with multiple applications.