Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Post History

#1: Initial revision by user avatar wizzwizz4‭ · 2021-08-14T16:33:10Z (about 3 years ago)
Each term of that product gives the size of the pool _when you pick an object out_ – it's the number of possible items you can pick out at that moment, if you're picking them one at a time.

Once you've taken $k$ items out of a pool of $n$ items, there are $n - k$ objects left over. This means that, when you were picking the last item out, your last item was also in the pool, giving a final term of $(n - k) + 1$.

---

I find the easiest way to get an intuition for something like this is to derive it from first principles. Mathematics only works for real-world problems when there's a relation between the problem and the mathematics, but it goes the other way, too: if some mathematics solves a problem, and you try to solve the problem from scratch, you'll end up doing something equivalent to that mathematics. If your solution is intuitive to you, then that intuition also applies to the mathematics.

Ultimately, the solution to a “this is not intuitive” problem is specific to the way you think. That also means such questions probably aren't appropriate for this site; consider asking a teacher instead.