imma need a bit of the help

[ALine]

Ok, so I'm taking discrete mathematics this semester and I cannot....can not, for the life of me understand the basics of counting. I was in class an the professor was talking and everyone was agreeing and I was sitting there wondering about how many fries can go with a shake, because I saw my future and it involved flunking out of college *little bit of humor there* . Any help, any would be appreciated in understanding the concepts of counting.

The first thing that I need help on is understanding the core principles behind the product rule and how it relates to set theory so that I can at least have some reference. 

Edited August 28, 2020 by ALine
added "little bit of humor there"

[joigus]

The only thing I can tell you is that I was never able to understand much at class. All the lights came later.

And some people are nodding because they're falling asleep. When one doesn't understand something one always assumes everybody else does.

Don't give up. 

[ALine]

thanks man, I have been working on it and I think I am starting to understand the product rule more clearly. 

Here is the statement I am currently working with...

" Suppose that a procedure can be broken down into a sequence of two tasks. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n2 ways to do the second task, then there are n1*n2 ways to do the procedure."

Below is a picture of how I am currently interpreting it. I think you need to split up the procedure into multiple sub procedures or "tasks" and there are n number of ways to do the first task and for each of those n1 number of ways to do the first task there are n2 number of ways to do the second task. I am starting to get it however I having problems digesting it conceptually.

 

 

[studiot]

Are you looking for an explanation of something like this ?

 

Sorry about the scan quality but I have to rush it right now.

 

[pzkpfw]

1 hour ago, ALine said:

...

" Suppose that a procedure can be broken down into a sequence of two tasks. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n2 ways to do the second task, then there are n1*n2 ways to do the procedure."

...

 

Personally I'd just go for a simple tree:

 

[ALine]

ok, that makes more sense

[ALine]

@studiot naw its cool in terms of you being in a rush and having to scan it through quickly, I'm going to need a minute to read through it and comprehend it.

 

and yes some thing like that but also being able to expand the concept of set theory to all counting problems.

Edited August 29, 2020 by ALine
added words to the first section