A community for students.
Here's the question you clicked on:
 0 viewing
shubhamsrg
 3 years ago
Binomial question:
simplify :
C(50,0) * C(50,1) + C(50,1) * C(50,2) .....+C(50,49) * C(50,50)
C(n,r) has the usual meaning i.e. n(combination)r
shubhamsrg
 3 years ago
Binomial question: simplify : C(50,0) * C(50,1) + C(50,1) * C(50,2) .....+C(50,49) * C(50,50) C(n,r) has the usual meaning i.e. n(combination)r

This Question is Closed

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0there are 4 options, though C(50,25) is an option but the ans given at the back is C(100,51)

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1sorry i actually need to prove it it should be C(2n,n1) or C(2n,n+1) hence answer is correct ..

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1first we use (1+x)^n (x+1)^n =(1+x)^(2n) i am actually very lazy in writing ... can u check that the LHS of ur question is just the coefficient of x^(n1) hence from RHS we need the coefficient of x^(n1) which is C(2n,n1) here n=50 hence C(100,49) =C(100,10049)=C(110,51)

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1a more genaralised result is C(50,0) * C(50,r) + C(50,1) * C(50,r+1) .....+C(50,nr) * C(50,50) = C(2*50,50r) though it can be generalised further but u can proceed as above...

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0i shall get back to you,,please gimme some time..

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1as i hardly remain online...

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0well,,i tried but i couldnt understand the concept really sir,,but i rote the formulla ! :P next ques was C(50,0) ^2 + C(50,1) ^2. .....(C(50,50) ^2 so according to the formulla,,r=0 and on plugging in that, we get the right ans i.e. C(100,50) but what about this kind ques : C(100,0)* C(200,150) + C(100,1) * C(200,151) ..... C(100,50) * C(200,200) ?

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1here u take (1+x)^100 *(x+1)^200 =(1+x)^300

matricked
 3 years ago
Best ResponseYou've already chosen the best response.1is LHS the coefficient of x^50 then from RHS u need the coefficient of x^50 ( if i am wrong just find the proper power of x) hence coefficient of X^50 in RHS is C(300,50) or C(300,150) is the ans correct

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0C(50,0) * C(50,1) + C(50,1) * C(50,2) .....+C(50,49) * C(50,50) C(50,0) * C(50,49) + C(50,1) * C(50,48) .....+C(50,49) * C(50,0) http://en.wikipedia.org/wiki/Vandermonde's_identity

KKJ
 3 years ago
Best ResponseYou've already chosen the best response.0C(50,0) * C(50,1) = C(50,49) * C(50,50) C(50,1) * C(50,2) = C(50,48) * C(50,49) C(50,2) * C(50,3) = C(50,47) * C(50,48) etc

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0let \( r=49\) C(50,0) = C(50,50) C(50,1) = C(50,49) C(50,2) = C(50,48) ... the expression is like \[ \sum_{k=0}^{50}\binom{50}{k} \binom{50}{49k}\] you can directly apply Vandemonde's identity to get \[ \binom{100}{49} \text{ or } \binom{100}{51}\]

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0Woops \[ \sum_{k=0}^{49}\binom{50}{k} \binom{50}{49k} \]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.