Permutation and Combination

[south urchin]

Not sure how, or did i miss something?

[eternal sentinel]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[south urchin]

2

[dapper steppe]

heya could u tell me the ans rq?
lemme see if i got it right..

[south urchin]

i dont hav the ans yet, still try to find it and compare

[dapper steppe]

wait so is ur answer incorrect?

[south urchin]

my one not sure yet

[dapper steppe]

yk what, why is it 5c3, when i can clearly see a line of 6 points from which 3 can be selected such that the centre is not inside

here ive marked it

And 12 such can be formed right?

[south urchin]

yup.

[dapper steppe]

but in that way,
We get 12x6c3 which is 240

which is way more than the total

so hm

i am really confused by this

[south urchin]

can be like 2 of this.

that touch or include the centre

[dapper steppe]

it says include yep

so yeah

centre can be on the tri or inside

but not outside

thats what the question says

[south urchin]

yup

60 triangle (diameter)

[dapper steppe]

but im able to form triangles like this from that area i showed u (of 6 points)
so why is it not 6c3

we are selecting 3 points out of 6 possible options

[south urchin]

not 6c3 because i might calculate wrong💀

[dapper steppe]

I mean see,
if we use 6c3,

and do

then we get 240 💀

12 x 6x3

6c3*

unless..

[south urchin]

"loading...."

[dapper steppe]

Oh wait

[dapper steppe]

if we consider duets like this

like 2 regions at a time

wait

that doesnt make sense

my brain is being fried rn ;-;

[south urchin]

i trying to think like this

and multiply by 2

[dapper steppe]

nono, but that will include bad cases too right

like this

[south urchin]

ya, another way that calculate all the bad case

[dapper steppe]

and we dont want these
we want to subtract them from 220

[dapper steppe]

which is why im highlighting that region of 6 points

cuz the entirety of the 6 points has the bad cases

[south urchin]

yup, so gonna focus on that 6 point

[dapper steppe]

yeah

but u see,

the issue is

when we do 6c3,

6c3,

our answer is 20

And we need 12 times that right,
Cuz 12 regions like that is possible on the circle

so 12x20 is 240 😭

Which is uh

💀

[south urchin]

yaa, ggs

[dapper steppe]

mhm

its way over our range

which is breaking my brain rn

u have the ans key for this?

[south urchin]

dont hav yet

[dapper steppe]

Like just the answer i want
Not the whole steps

[dapper steppe]

ah rip ok ok

[south urchin]

maybe

[dapper steppe]

Thats kinda the same as what u did with 5c3

lol

I tried that too

and uh yeah got the same thing

im so confused

might ask my teacher tomorrow whats wrong with the 6c3 thought

[vivid ledge]

i got an answer

there are 6*10 triangles that use diagonals (6 possible diagonals and they can be joined with any of the other 10 points). we will count the ones that don't use diagonals now

start with an arbitrary point. like the one marked in red here

the fuschia scribble is the diagonal we can't use

there are 0 triangles we can form using the point directly to the right

and 1 with the next one over, and 2 with the next one (those are drawn as example) and so on

minding that we can't use diagonals

so that's 10 more triangles, and another 10 with the point diagonally opposite to the red one

now triangles that don't use those points and use the red point here:

there are 6 more, and another 6 using the diagonal point

actually hold on i forgot to add one case up

ok so another 3 + 3 here

then just 2 more with the last 6 points

so my answer is...

,calc 60 + 10 + 10 + 6 + 6 + 3 + 3 + 2

[frozen grotto]

Result:

100

[vivid ledge]

ok @south urchin i agree with your answer

this is not the quickest way to count, but it is good to count in different ways to see if they all agree

so i wanted to do something different

[south urchin]

Alright, thanks

[dapper steppe]

heya, so we did get the answer 100 a few times actually
however i really do wonder whats wrong in my thought process..

this is basically what i did

where we see a region of 6 points individually (Marked in red and purple)

And we do 12 times 6c3,

12 times as we do 2 x 6 (As 6 possible sets of such duets are possible)

but we get 240

which is uh kinda out of our range (12c3 = 220)

so like,
whats wrong in my thought process
im really curious

OH I THINK I GET IT NOW

OHH i have included repeated cases

oh oh oh i see

alright my bad

[south urchin]

.solved