24 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.well it kind of is a set rule
just like pascal's triangle
they just found a way to expand (a+b)^n and this is the method they created
and it worked so it's always been like that
Write (x+y)ⁿ as (x+y)(x+y)...(x+y) then you will figure it out.
Hmm that works too.
but in case of pascal's triangle the coefficients are always 1 for x and y
in binomial theorem there's questions for coefficients with x and y having coefficients
which is another story for now but this is the explanation, I guess
oh a blackboard
epic shi
your blackboard is so shiny
my teacher explained like "agar total terms n hai and usko do bando mein bantna hai r and n-r ki amounts me then we get the factorial from pnc and from there we get the coefficient formula of nCr"
@SirLancelotDuLac
r and r-1?
corrected
...
Yeah. Look at it this way (x+y)(x+y)...(x+y) mein n brackets hain. Now agar isse expand karke likhein toh $x^{a}y^{n-a}$ tabh aayega jabh n brackets mein se a brackets se x aur baakiyon se y multiply karein. So the number of ways for that is nCr
SirLancelotDuLac
The pascal triangle method is another way. Define $a{n,r}$ as co-effecient of $x^{r}$ in $(x+y)^{n}$. Not necessary but if you are interested try to solve this recursion: $a{n,r}=a{n-1,r-1}+a{n-1,r}$
SirLancelotDuLac
thoda thoda samaj aya but ithink yaad hi kr leta hu
:Saul_Goodman:
well I mean that much sort of obvious from the expression itself
he just told you in words
yaad karne se life mushkil hogi
abi sorted?
Nhi wait ek Baar phirse pdhata sable explanations
Cool
+solved @BlindSniper (BS) @SirLancelotDuLac
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