>>11081694Looking at two problems, which I am having trouble solving.
> CountingAssumptions: Order matters, repetition allowed
University has 14-day exam period. You are writing math, physics and stat exams. How many choices of days are possible if maths exam must be held at least two days earlier than physics, and physics exam must be held at least two days earlier than stat.
Naive thought was 14x12x10, but the 'earlier' key word was the sticking point. I'm thinking math can be taken on days 1-10, physics on day 12 and stat only on day 14. Though, perhaps that is also a naive way of looking at it. Really not sure how to model the problem.
> GroupsHow can you be sure that (Z_n3xZ_n3,+) has no more than 6 subgroups.
{(0,0)}
{(0,0),(1,1),(2,2)}
{(0,0),(0,1),(0,2)}
{(0,0),(1,0),(2,0)}
{(0,0),(1,2),(2,1)}
{(0,0),(1,1),(2,2),(0,1),(0,2),(1,0),(2,0),(1,2),(2,1)}
