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How to simply write what I just wrote, I don’t even know what to search [discrete math]
cristinagallach
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Jun 21, 2022
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How to simply write what I just wrote, I don’t even know what to search [discrete math]
learnmath
cristinagallach
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Jun 21, 2022
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Well that is hugely big.
You can alternatively express it as 19C10 × 18C9 × 17C8 × ... × 10C1
So you can break that down as
19! / (10!9!) × 18! / (9!9!) × ... × 10! / (9!1!)
There could be some simplification but it doesn't seem like it will be anything concise.
IgNarLoL
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Jun 21, 2022
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IgNarLoL
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there are a few ways, depending what you plan to do with it.
```
Π(n=1→10)( n choose 9 )
Π(n=1→10)( (20-n)! / 9!10! )
aCb := a! / b!(a-b)!
→ (19c9)(18c9)...(10c9)
= 19!/9!10! × 18!/9!10! × ... × 10!/9!10!
= 19!18!17!...10! / 9!¹⁰10!¹⁰
= 19!18!...11! / 9!¹⁰10!⁹
```
there are definitely others but these seem most useful?
ProFightLeague
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Jun 21, 2022
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ProFightLeague
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How about
Π[a=10..19] nCr(a, 9)
= Π[a=10..19] a! / (a-9)! / 9!
= 1/9!^10 · Π[a=10..19] Π[b=0..9] (a-b)
Basically, find all pairwise differences between natural [10,19] and [0,9] and multiply all of them together
PoliceNat51
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Jun 21, 2022
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PoliceNat51
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