There are 10 students taking an English class and 17 students taking a Math class.

Q1. A group consisting of 3 English students and 5 Math students must be formed. How many possible groups can be made?

Q2. An English student decides to join the Math class. (There are still 27 students in total, but now there are 10 students taking English and 18 students taking Math.) When forming the same group as mentioned in Q1, this particular student can be selected as either an English student OR a Math Student, or may not be selected at all. How many possible groups can be made after this change?

Q3. If yet another English student decides to join the Math class (10 English students, 19 Math students), what will the number of possible groups be now?