If I want to work for these companies, what is a good major to get and would a ba in information technology with a minor in design be ok?
Depends on the kind of job. The design and development jobs would mostly be done by those who studied CS (as opposed to IT).
It depends on what you want to do. All of those companies hire people to manage IT for their computing systems, so if you wanted to work in IT (as in, managing the computer systems that people at Google et al. use to get their work done), then a major in information technology could be a good bet. (These companies also hire people in all kinds of fields - like human resources/people operations, technical writers, marketing/sales directors, data scientists, recruiters, etc. While the bulk of their employees and the heart of the organization are most likely engineers, you don’t have to be an engineer to work at any of these companies).
If you want to be a software developer or engineer at these companies, then no, a major in IT is not a good bet - you want to major in something more akin to computer science.
Ok what if I wanted to work for apple?
Go to Jobs at Apple and look at their job openings. You will see that @ucbalumnus and @juillet have correctly stated what those companies are looking for: software and hardware engineers. IT descriptions seek software engineers which are usually CS majors.
As a side note, it might be a good idea not to fixate too much on one particular company - much less select your college major on that basis. These companies are very prestigious and desirable ones to work for; there are thousands of people who want to work for them. Google says they get hundreds of thousands of applications every year. It’s great to say that you want to work for one of these companies, and if you do a CS major (or engineering) is probably your best bet because the majority of the people they hire are going to be software developers and engineers.
But it makes no sense to major in CS with the goal of working for one of these places if you don’t want to to do that. Then you’ll be miserable in your job! If you want to major in IT, major in IT. That field has good prospects; worry about exactly which company you’ll work for later.
They like to recruit from MIT and Stanford goodluck.