Pascal Triangle Struggle (High School Data Management)

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[summer sage]

Each level represents how many letters you can choose

[balmy remnant]

Yeah, i think i have the answer but i counted manually. There was another problem like thyis with boxes, where i counted the paths and added them up when there was a new one.

Im just struggling to find the easiest way to calculate all paths

Specifically in this format, the mitchell one

[summer sage]

I think you're overcomplicating it

in the first level there is 1 way to choose M

in the second there's 2C1 which is just 2 ways of choosing I

so there's 2 ways of spelling MI as it's 1x2

[balmy remnant]

Yeah and it smooth until theres the H's

Just gets hard when the one H can be chosen more than the edge H's

[summer sage]

Wdym

[balmy remnant]

I believe theres 4 ways of spelling MITC

[summer sage]

yeah

[balmy remnant]

But its not 4x3 because there isnt 12 ways of spelling MITCH

I think?

[summer sage]

how so

[balmy remnant]

Because each C goes to 2 different H's

Oh

Ig it would just be 16 then

[summer sage]

is there a restriciton on the path

like does the letter above need to be directly below

[balmy remnant]

No

[summer sage]

there are 3 ways of choosing H (once)

3C1

[summer sage]

Yep

do you see how there's two paths to the middle H

[balmy remnant]

Yeah

[summer sage]

that's basically double counting

[balmy remnant]

What do you mean

[summer sage]

well not double counting

but your method is wrong

the two C's act as 1 element

since we are only choosing 1 C

[balmy remnant]

Yeah

[balmy remnant]

But the question asks for every way to spell mitchell

[summer sage]

yeah

[balmy remnant]

So the C's arent the same

Each one counts for a different spelling

[summer sage]

we counted for that before

2 ways of choosing C

[balmy remnant]

Oh

Okay i think i get it now

[summer sage]

btw it's be more like this

6 branches

[balmy remnant]

But thats wrong right

The 6 brances

Braches

[summer sage]

well it's just a different method

[balmy remnant]

Okay tell me if this makes any sense

We combined the C's

[summer sage]

yea

[balmy remnant]

Is that similar to the idea of like

Okay tehre was a question in an earlier lesson that was spellings for 'EXETER'

and each E was combined, so the answer ended up being 7!/4!

Or 3! sorry

because each e was combined

same idea right?

[summer sage]

Hm, that's permutations

[balmy remnant]

yeah

[summer sage]

this is combinations

[balmy remnant]

indeed

Im just trying to make sense of it in my head

[summer sage]

because this type of question doesn't specify the ordering of the letters

[summer sage]

yeah it's 3!

there's 3! ways of rearranging {E,E,E}

[balmy remnant]

i thought it did specify the ordering of the letters

it has to be M I T C H in order? or do you mean something else

[summer sage]

No, as in we aren't counting the number of ways each letter can be rearranged

like MITHC, MIHTC etc...

[balmy remnant]

Yeah

This is what i have down rn

1, 2, 2, 4, 12, 24, 72, 72 if thats easier

[summer sage]

Seems correct

[balmy remnant]

Perfect

Seems to make sense

Thanks

[summer sage]

np