How many combinations of students are possible?

Question

There are 30 students in a history class. Twenty percent of the students are randomly chosen to participate in a teacher evaluation 

Answer 1

20% of 30 is 6 are randomly selected.

 

30 choose 6 = 30! / (30-6)! 6! 

 

                  = 30! / 24!6!

 

                  = 30 * 29 * 28 * 27 * 26 * 25 

                    --------------------------------- <-- 24! cancels

                     6 * 5 * 4 * 3 * 2 * 1

 

                  = 29 * 28 * 27 * 26 * 25

                   ---------------------------------- <--- 30 = 6 * 5 cancels

                       4 * 3 * 2 * 1

 

                 = 29 * 7 * 9 * 13 * 25   <--  4 cancels 28, 3 cancels 27, 2 cancels 26

 

                = 593775