Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

shubhamsrg

  • 2 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
  1. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there are 4 options, though C(50,25) is an option but the ans given at the back is C(100,51)

  2. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry i actually need to prove it it should be C(2n,n-1) or C(2n,n+1) hence answer is correct ..

  3. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    first 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^(n-1) hence from RHS we need the coefficient of x^(n-1) which is C(2n,n-1) here n=50 hence C(100,49) =C(100,100-49)=C(110,51)

  4. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a more genaralised result is C(50,0) * C(50,r) + C(50,1) * C(50,r+1) .....+C(50,n-r) * C(50,50) = C(2*50,50-r) though it can be generalised further but u can proceed as above...

  5. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i shall get back to you,,please gimme some time..

  6. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if possible sure ..

  7. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    as i hardly remain online...

  8. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well,,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) ?

  9. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here u take (1+x)^100 *(x+1)^200 =(1+x)^300

  10. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay,,following..

  11. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sir ? hmm..?

  12. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is 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

  13. KKJ
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nCr = nC(n-r)

  14. experimentX
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    C(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

  15. KKJ
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    C(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

  16. experimentX
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    let \( r=49\) C(50,0) = C(50,50) C(50,1) = C(50,49) C(50,2) = C(50,48) ... the expression is like \[ \sum_{k=0}^{50}\binom{50}{k} \binom{50}{49-k}\] you can directly apply Vandemonde's identity to get \[ \binom{100}{49} \text{ or } \binom{100}{51}\]

  17. experimentX
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Woops \[ \sum_{k=0}^{49}\binom{50}{k} \binom{50}{49-k} \]

  18. shubhamsrg
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you :)

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.