In a small MBA class, each of the 6 students must write a report on one of their 8 lectures. In how many different ways can they each choose one of the lectures

Question

In a small MBA class, each of the 6 students must write a report on one of their 8 lectures. In how many different ways can they each choose one of the lectures if: (a) No 2 students may choose the same lecture? (b) There is no restriction on there choices?

Answer 1

In either case, the choices are multiplied to get the final answer.

 

 

If each student has 8 choices, then there are 8^6 = 262,144 possible combinations.  Each choice is an independent event, and does not depend on any other choice.

 

In the first case, each student after the first has fewer choices available---i.e. the 1st student has 8 possibilities, the 2nd student has 7, etc. 

With 6 students, there are 6 terms:

8 x 7 x 6 x 5 x 4 x 3 = 20,160

 

To be rigorous, we would say that there are 8! possible choices, but that the last two are not taken.  Thus we have 8! / 2!  (the answer is the same.)