2. Solution: Since all 1200 students have joined at least one extracurricular group, the number of students who did not join any group is 0. We use $A_{1}, A_{2}, A_{3}$ to represent the sets of students who joined the math group, the Chinese group, and the English group, respectively. Thus, by the problem statement, we have
$$\left|A_{1}\right|=550,\left|A_{2}\right|=460,\left|A_{3}\right|=350$$

We also use $A_{12}$ to represent the set of students who joined both the math and Chinese groups, $A_{13}$ to represent the set of students who joined both the math and English groups, and $A_{23}$ to represent the set of students who joined both the Chinese and English groups, then we have
$$\left|A_{13}\right|=100, \quad\left|A_{12}\right|=120$$

We use $A_{123}$ to represent the set of students who joined all three groups, then
$$\left|A_{123}\right|=140$$

Noting the initial explanation, by Theorem 1 of this chapter, we get
$$\begin{array}{c}
0=1200-\left|A_{1}\right|-\left|A_{2}\right|-\left|A_{3}\right|+\left|A_{12}\right| \\
+\left|A_{13}\right|+\left|A_{23}\right|-\left|A_{123}\right|,
\end{array}$$

Thus, we have
$$\begin{aligned}
\left|A_{23}\right| & =-1200+550+460+350-100-120+140 \\
& =80
\end{aligned}$$

That is, the number of students who joined both the Chinese and English groups is 80.
2. A school organized three extracurricular activity groups in mathematics, Chinese, and foreign language. Each group meets twice a week, with no overlapping schedules. Each student can freely join one group, or two groups, or all three groups simultaneously. A total of 1200 students participate in the extracurricular groups, with 550 students joining the mathematics group, 460 students joining the Chinese group, and 350 students joining the foreign language group. Among them, 100 students participate in both the mathematics and foreign language groups, 120 students participate in both the mathematics and Chinese groups, and 140 students participate in all three groups. How many students participate in both the Chinese and foreign language groups?