What are my chances of working in business/computer field if I'm a Liberal Arts Major?

I’m a senior about to graduate from high school and I’ve decided to pursue an English degree. I’m going to be smart about it, though. I’ll double minor in business and marketing, take as many classes in computer science and maybe graphic design as I can, and if necessary get a certificate in computing. All of this will be done to make me look more employable, despite my decision to be a liberal arts major.

My sister majored in MIS and she now works as a Systems Analyst. I asked her about her field and she said that there are people who she works with who were liberal arts majors that minored in computer science. The college I’m planning on attending doesn’t have computer science as a minor, only as part of a certificate program, so that’s what I was going to go after I get my degree (it’s a year program). And could I get accepted into an MIS grad program if I wanted to further my education even though I wouldn’t be a business major (would minoring in it count)? Does this sound like a good plan?