How many different groups of students can show up for a seminar with an enrollment of 11

Question

amistre64 · Answer

you usually need to have a number of students in order to determine all the different combinations

directrix · Answer

I am thinking of the problem in the following way:

0 students could show up in C(11,0) = 1 where C(11,0) means a combination of 11 taken zero at a time.

To that add, C(11,1) = 1 which is the number of ways exactly one student of the 11 could show up for the seminar. 

To that add, C(11,2) = 55 which is the number of ways exactly two students of the 11 could show up for the seminar.

Continue in that pattern until you complete C(11,11) = 1 which is the number of ways that exactly 11 (or all) of the 11 students could show up for the seminar.

You can crank out these numbers or get them from the 11th row of Pascal's Triangle. See the attachment.  The sum should be a power of 2.

@kondrose1