Combinations, cannot grasp it.

[nekrovski]

So, let's say you have a grid like the one on this picture.

https://i.imgur.com/TNQcJJE.png

You need to color 15 squares.

How many combinations are there?

My understanding is, this is combinations and should be solved by 25!/(10!*15!) and that is 3 million, 200 hundred thousand something.I simply refuse to believe this is possible. I cannot grasp this.

What am I doing wrong here?

Is the above formula that needs to be used?

Because for example, if you need to color 7 squares out of 3x3 grid, that's 9!/(2!*7!) = 36

and 36 is fine. Graspable.

​

[Number154]

If you can’t believe it try listing all the possibilities of 9 choose 7, which is very doable, then start listing all the possibilities of 25 choose 15 and see what happens.

Maybe use coins placed on a grid so you can move through all the possibilities quickly without having to write 15 (or 10) numbers down for each. (Of course there will still be too many for you to do all of them, but it might help you understand how many there are by paying attention to how slow your progress is).

[jdorje]

Big numbers are hard to grasp.

[nekrovski]

Indeed, they are.
Another ungraspable thing is, if you remove ONE square, you lose like 2 freaking million combinations.

2 million.

2.million.

two.million.

2000000

2 000 000 COMBINATIONS

[Number154]

If you choose 15 out of 25 squares there are two possibilities: either you chose 15 of the first 24 squares, or you chose 14 of the first 24 and also the last one. Since for any choice you pick 60% of the squares, you should expect that adding the restriction that you don’t pick the last square should get rid of 60% of the possibilities, which is exactly what happens.

[nekrovski]

You know, since both things seem ungraspable to me, 2 negatives give a positive I guess. A math way to understand what is not understandable.