Differents ways of ordering bars and stars

[LCSphysicist]

Homework Statement

How many different ways can we plop down the stars and bars?

Relevant Equations

...

Actually, the answer is

But i am not sure why we can apply combination here. I am a little confused.
I could get the answer fixing the bar 1 in each place, with this fixed, we could change the position of the other bar. That would be:
First we have 7 different position
After this, 6 different position
5
.
.
.
0

Sn = 8*(7+0)/2 = 28

But i don't know why this is a combination.
Technically, is not
***|*|** = ||****** in the point of view of combination (The order does not matter)?

 

[fresh_42]

You can look at it different ways. You counted possibilities, and the other way is what the book does: Each of the eight places has two possibilities. That is drawing eight times either a ball with a star or with a bar out of the bowl and putting back the drawn ball. So we have eight places and two balls, which is 8 choose 2.

 

[Ibix]

If I affix numbers 1-6 to the stars and 1-2 to the bars, so they are all distinguishable, how many distinct orderings are there?

If I removed the numbers from the bars, for any given layout how many became indistinguishable from it? So how many distinguishable arrangements are there?

If I then removed the numbers from the stars (so neither stars nor bars are distinguishable), for any given layout how many became indistinguishable from it?

 

[etotheipi]

The question is equivalent to asking "how many distinct subsets of size 2 can I form from the set $\{1,2,3,4,5,6,7,8\}$?"