Find the number of different groups containing an odd number of students that can be chosen from a group of

(i) 3 students

(ii) 5 students

(iii) 7 students

(iv) Suggest a general formula for the number of of different groups containing an odd number of students that can be chosen from a group of n students, and prove that your formula is correct.

Bonus: repeat the question above but for groups containing an even number of students.