#. Let P be the set of people in a group, with |P| = p. Let C be a set of clubs formed by the people

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tame pollen
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uh need help

obsidian martenBOT
tame pollen
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. Let P be the set of people in a group, with |P| = p. Let C be a set of clubs formed by the people in this group, with |C| = c. Suppose that each club contains exactly g people, and each person is in exactly j clubs. Use two different ways to count the number of pairs (b, h) ∈ P × C such that person b is in club h, and deduce a combinatorial identity.

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so far what i got

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is that u can multiply p by j

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can say that

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there are pj people

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who belong in 1 club

sonic talon
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...no, there are p people.

tame pollen
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ye

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i mean like

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u could say that since there is p people who belong in j clubs u can multiply and say there is pj people who belong in 1 club

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does that make sense?

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or

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cuz sometimes im just dumb

sonic talon
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...no, because either there are p people who belong to 1 club or there are 0 people who belong to 1 club, depending on whether g = 1.

tame pollen
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uh

sonic talon
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Wait, j.

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Whether j = 1.

tame pollen
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im lost

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from what i understand the question said there are p people in a group and those p people belong to j clubs. the total amount of clubs is c and each h has g members

sonic talon
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...yes. Everyone is in j clubs. Therefore, if j = 1, then everyone, which is p people, is in 1 club, and if j =/= 1, then nobody, which is 0 people, is in 1 club.

tame pollen
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OH WAIT

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BRUH

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SO LIKE

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I KINNA ALEADY MADE AN EQUATION

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WHIHC WAS P = CG

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BUT

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THERE ARE REPITIONS

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SO I WANTED TO GET RID OF THAT

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AND SO LIKE

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can u gimme a sec to like

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think how to say this

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BASICALLY IF U HAVE 10 PEOPLE WHO HAVE TO JOIN 2 CLUBS ITS THE SAME AS 20 PEOPLE JOINING 1 CLUB

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which

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i think

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may lead onto

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removing the repititins

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and btw

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im tryna make a formula for th e amount of people

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uh

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oh wait im sped

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why am i makiing a formula

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with p in it

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if im tryna solve for p 😭

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i mean ig could make a formula

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AND GREATIM STUPID AGAIN

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I FORGOT THE REASON I WAS DOING THIS IS TO ANSWER FIRST QUESTION NOT THE COMBINATORICAL IDENTITY THINGY

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BRU

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so like

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the part im stuck on

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is

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i made solution equal to (\binom{pj}{g})

tulip ventureBOT
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TheSkittleMonster

1188252544212926507.png
tame pollen
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but llike

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wait

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i mad e solution equal to

sonic talon
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Frankly, it sounds like you don't actually understand what you're doing.

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Like you're just kind of flailing about and guessing.

tame pollen
sonic talon
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So in math, what we actually do is we start from what we know is true, and then we move forward towards what we know must be true.

tame pollen
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(\binom{pj-rg}{g} with the capital pi thingy and r=0 with n=pj/g)

tulip ventureBOT
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TheSkittleMonster

1188252544212926507.png
sonic talon
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...what?

tame pollen
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bruh idk how to make spaces

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but

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since if u have

sonic talon
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Okay, but that's only part of why I said "what".

tame pollen
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10 people in a group and 2 clubs u can say 20 people can join 1 club. now for one club there is 20 choose s possibilities the next is 20 - s choose s possibilities and so on

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but im not sure if i add or multiply them together

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and the solution i put doesnt mathc 😭

sonic talon
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What are you even talking about? Remember what I said? Move forward from what is true to what must be true? What are you even counting here?

tame pollen
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this is combinatorics btw

sonic talon
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I know that.

tame pollen
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oh

sonic talon
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Do you think I'd even be here if I didn't?

tame pollen
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idk i just saw ur roles