39 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.what is this question It seems simple but I am not able to deduce anything💀
(it's a proof btw. You need to prove LHS = RHS)
Ik:sweaty:
same lmao
@Opt just to know your thought process, how did you even start on 42
With a huge mess lol
I expanded everything, tried to reform stuff.
lmao fair
but the summation 💀
$t{r} = \binom{m}{r}\binom{n}{r}\binom{p+r}{m+n}
t{r} = \frac{m!n!(p+r)!}{(r!)^{2}(m-r)!(n-r)!(m+n)!(p+r-m-n)!}$
Shifting stuff,
$\binom{m+n}{m}t_{r} = \binom{p+r}{r,r,m-r,n-r,p+r-m-n}$
if the solution is even vaguely similar to this i will cry
also wow you're good at latex
Gods no wait
That last line is so wrong
its fine 💀
Opt
Compile Error! Click the :errors: reaction for more information.
(You may edit your message to recompile.)
There we go
RHS is a multinomial coefficient
dear god
So i tried expressing it as coeff of so-and-so in an expansion
And it went wrong very quickly.
this is so far above jee level its actually hilarious
@SirLancelotDuLac you're the last hope
It's Lance's JEE today
Worst day possible to find this monster
yeah yeah, if he feels like it when he gets back
lmAO
Oh wait that font too. Is this Principles and Techniques in Counting? 😃
Damn its been far too long since I did this stuff.
https://math.stackexchange.com/questions/1460712/li-shanlans-combinatorial-identities (Hope this helps)
Mathematics Stack Exchange
Li Shanlan's combinatorial identities
I am struggling to prove the following combinatorial identities:
$$(1)\quad\sum_{r=0}^m \binom{m}{r}\binom{n}{r}\binom{p+r}{m+n} = \binom{p}{m}\binom{p}{n},\quad \forall n\in\mathbb N,p\ge m,n$$
$$...
Yup it's Chen Chuan Chong
Yeah, its a pretty good book.
What sort of demon thinks these up?
Yeah but maybe some combinatorial proof would be easier for this imo.
'Cuz RHS seems pretty straight forward (for 42nd)
It does, but the LHS is a sum
I have a feeling it's some kind of path, with varying position of fixed points, but I have no clue
Btw, how was the Combinatorics in your paper?
Crap. I did literally everything and forgot to do '-1' for one case. :/
Man, that hurts soo much.
Overcounting hurts real bad
Integer type?
No, mcq.
And the option was present?
Yeah.
I stopped checking the paper after that.
Oof thats gotta hurt
How much you expecting?
I absolutely have no idea.
Just hoping God has mercy 🙏
Understandable. One of my friends said he wouldn't even check the answer key. Direct results.
This is what I'm planning to do.
we good? @Opt
+solved @SirLancelotDuLac
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