I'm currently entering my third year of undergrad at a state university in the United States. I originally went to school for computer engineering but halfway through the past year I realized I was very interested in math. My school offers a program for a math major with an "emphasis in another field", so in conjunction with my engineering degree it will only require me to take a few extra courses I otherwise wouldn't have taken to get my BS in mathematics. The engineering/math double major was my plan up until a few weeks ago.
I've spent the summer interning as a software engineer and have really enjoyed the work I've been doing. The college of engineering at my university requires us to pick an "elective focus area" and the area I've picked is software engineering. I was looking at the requirements for a computer science degree and realized that between my math major and careful selection of electives, it is very feasible that I could satisfy all of the requirements for a degree in engineering, math, AND computer science while still finishing school in four years.
My question: how will having three undergraduate majors affect my chances at future job prospects? I've been warned that pursuing a Masters without any work experience can be potentially detrimental because employers believe they have to pay you more.
I should mention that I believe my actual engineering degree will be an electrical engineering degree that may have some notation about a computer track of study (to be honest, I'm not exactly sure; I need to speak with my adviser about this). Having the computer science degree would help ensure that I'm able to find work in the field I want, but I don't want employers to discredit my education.