A Salem college has 300 students, and 20 take none of three electives. The note gives each elective's total, and 50 students take exactly two electives. How many take all three?

At least one $=300-20=280$. The totals add to $130+110+120=360$, which counts exactly-two students twice and all-three students three times: $360=280+50+2T$, so $2T=30$ and $T=15$. 30 forgets to halve, 10 divides by 3 instead of 2, and 80 ignores the 50 students who take exactly two.