I guess a better question is if they enjoy what they do.
Yes, they do. I think only one of them isn't too keen on it.
I'm curious now. What are the house placements of these Cancer people?
I don't know all of their birth times but here is what I know:
1. Cancer Sun in the 8th house, Pisces Moon in 4th house, Scorpio Rising, Mercury in Leo in 9th, Mars in Cap in 3rd
(yup, this is my bf -- software engineering)
2. Sun/Mercury in Cancer, Scorpio Moon, houses unknown
3. Cancer Rising, Aquarius Moon in 8th house, Mercury in Scorpio, Sun in 4th
4. Cancer Sun, Virgo Moon, Cancer Merc, houses unknown
5. Sun/Mercury in Cancer in 3rd house, Scorpio Moon in 7th, Taurus Rising, Venus conjunct Mars in Leo in 5th house
We don't stereotype Cancers as having technical aptitude, sure, but I work in a very solitary environment, mostly only interacting with my boss on a daily basis, who I like, so it isn't a problem. Programmers are probably going to either work alone or on tight-knit teams so it's probably a comfortable environment for a reserved/cagey person whose major Cancer placement is in one of the more introverted houses.
I think the ideas about Cancer may need to be revamped. A lot of Cancers I know are great with tech, math, etc. I thought it was due to their proximity to Gemini but very few of the ones I know have any Gemini.
I was thinking about why they might be attracted to this field and yes, I came to the same conclusion. Being able to work alone or in small groups, with minimal outside interaction would be fitting for their placements.
Back to Sagittarius, I'm not sure a 4th house Sag would want to be a teacher, for example. The amount of people you have to interact with as a teacher might be tiring.
Sagittarius produces interesting people and thus interesting careers when it is one of the less outgoing houses.