Question

Thirteen students want to ask for their teachers help, but they won't all fit in the teachers room. Therefore, they need to choose a representation of students to visit him. How many different groups with at least one student and at most twelve students can the thirteen students choose among themselves?

Answer 1

One student can be chosen as a representative out of the 13 students in 13 ways

Two students can be chosen as representatives out of the 13 students in 13C2 ways

Similarly, twelve students can be chosen in 13C12 ways

Thus, number of different groups possible

= 13C1 + 13C2 + 13C3 + ............ + 13C12

=

=

= 8190