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arindameducationusc

  • one year ago

Challenge and also a help..... Check image for question

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  1. arindameducationusc
    • one year ago
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  2. arindameducationusc
    • one year ago
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  3. arindameducationusc
    • one year ago
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    @ganeshie8 uploaded

  4. ganeshie8
    • one year ago
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    look at the 10th row in pascal's triangle : |dw:1438086192297:dw|

  5. ganeshie8
    • one year ago
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    We want to find \(x\) such that \[\large ^{10}C_{x-1} - 3 *^{10}C_{x}~\gt~ 0\]

  6. arindameducationusc
    • one year ago
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    yes i m looking

  7. ganeshie8
    • one year ago
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    |dw:1438086392992:dw|

  8. arindameducationusc
    • one year ago
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    yes >0 , understood that because sqare root function and denominator

  9. ganeshie8
    • one year ago
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    notice that 45-3*10 > 0 10-3*1 > 0 1 - 3*0 > 0 so, x = 9, 10, 11 are fine

  10. arindameducationusc
    • one year ago
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    The answer is none of these... so I am confused

  11. ganeshie8
    • one year ago
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    x = 8 doesn't work because 120 - 3*45 < 0 similarly x>11 doesn't work because 0 - 3*0 = 0

  12. ganeshie8
    • one year ago
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    answer is \(a\) to my knowledge

  13. arindameducationusc
    • one year ago
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    let me analyse once, give me some time then I may ask you if you have no problem @ganeshie8

  14. ganeshie8
    • one year ago
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    sure

  15. arindameducationusc
    • one year ago
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    Is this the language for combinations? Thats interesting.... hmmm...

  16. arindameducationusc
    • one year ago
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    solve (10 choose (x-1)) - 3*(10 choose x) > 0 over integers Can you explain this sentence with respect ot combination?

  17. arindameducationusc
    • one year ago
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    #to#

  18. ganeshie8
    • one year ago
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    \(\large ^nC_r\) is read as \(\large n~~\text{choose}~~r\)

  19. ganeshie8
    • one year ago
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    it is called binomial coefficient and represented by symbol : \[\large \binom{n}{r}\]

  20. arindameducationusc
    • one year ago
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    Each of the different groups or selections which can be made by taking some or all of a number of things(irrespective of order) //Can you please elaborate this sentence

  21. arindameducationusc
    • one year ago
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    // Its for Combination

  22. arindameducationusc
    • one year ago
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    45-3*10 > 0 You checked this for 9?

  23. ganeshie8
    • one year ago
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    yes that is for x = 9

  24. ganeshie8
    • one year ago
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    suppose you went for shopping and liked 5 shirts

  25. arindameducationusc
    • one year ago
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    ok

  26. ganeshie8
    • one year ago
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    but you can only buy 3 of them

  27. arindameducationusc
    • one year ago
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    ok

  28. ganeshie8
    • one year ago
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    how many ways are there to choose 3 shirts from the 5 shirts ?

  29. ganeshie8
    • one year ago
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    for definiteness, lets call the shirts : \(a,~b,~c,~d,~e\)

  30. arindameducationusc
    • one year ago
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    calculations say 10

  31. ganeshie8
    • one year ago
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    can you list them all ?

  32. arindameducationusc
    • one year ago
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    ok go on... nice

  33. arindameducationusc
    • one year ago
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    no, I don't have that strong concept.... I would definitely understand from you.... nice....

  34. ganeshie8
    • one year ago
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    no, just list them all, its a simple counting problem

  35. ganeshie8
    • one year ago
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    you can buy the shirts \(a,b,c\) or \(b,c,d\) or \(c,d,e\) or ... try listing them all

  36. arindameducationusc
    • one year ago
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    okay ... abc acd bed bcd ade bec cde aeb

  37. arindameducationusc
    • one year ago
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    more two

  38. ganeshie8
    • one year ago
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    looks two are missing yeah

  39. arindameducationusc
    • one year ago
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    I am trying :P

  40. arindameducationusc
    • one year ago
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    bae

  41. arindameducationusc
    • one year ago
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    no no not bae

  42. ganeshie8
    • one year ago
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    ``` {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} ```

  43. ganeshie8
    • one year ago
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    \(\large ^{5}C_3\) gives the number of ways you can choose 3 shirts from 5

  44. arindameducationusc
    • one year ago
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    Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there?

  45. arindameducationusc
    • one year ago
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    ##found##

  46. ganeshie8
    • one year ago
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    i hope you're familiar with the formula for computing \(^5C_3\) : \[^5C_3 = \dfrac{5!}{3!(5-3)!} =\dfrac{5!}{3!*2!}= \dfrac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1*2\times 1} = 10\]

  47. arindameducationusc
    • one year ago
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    yes yes.... ofcourse

  48. arindameducationusc
    • one year ago
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    I am talking about counting.. thats hard! :P

  49. ganeshie8
    • one year ago
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    `Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there?` hey i didnt get what you're asking..

  50. arindameducationusc
    • one year ago
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    suppose abcdefgh and we have to choose 3 pairs then is there any way by counting? Like suppose I want to view all possibilities

  51. ganeshie8
    • one year ago
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    you want see the entire list of 56 choices ? ``` {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} {a,b,f} {a,c,f} {b,c,f} {a,d,f} {b,d,f} {c,d,f} {a,e,f} {b,e,f} {c,e,f} {d,e,f} {a,b,g} {a,c,g} {b,c,g} {a,d,g} {b,d,g} {c,d,g} {a,e,g} {b,e,g} {c,e,g} {d,e,g} {a,f,g} {b,f,g} {c,f,g} {d,f,g} {e,f,g} {a,b,h} {a,c,h} {b,c,h} {a,d,h} {b,d,h} {c,d,h} {a,e,h} {b,e,h} {c,e,h} {d,e,h} {a,f,h} {b,f,h} {c,f,h} {d,f,h} {e,f,h} {a,g,h} {b,g,h} {c,g,h} {d,g,h} {e,g,h} {f,g,h} ```

  52. ganeshie8
    • one year ago
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    as you can see its not so pleasant to list them all... why would you want to do that lol

  53. arindameducationusc
    • one year ago
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    ofcourse it is unpleasant! but Maths is Maths.... but can you tell me how did you do it?

  54. arindameducationusc
    • one year ago
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    Can Wolfram do this?

  55. ganeshie8
    • one year ago
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    https://jsfiddle.net/ganeshie8/r2hjr3js/1/

  56. arindameducationusc
    • one year ago
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    Thank you so much for giving your precious time.... :)

  57. ganeshie8
    • one year ago
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    comb(n, set) lists all the combinations of size "n" from the set "set"

  58. ganeshie8
    • one year ago
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    but trust me, you almost never want to list all the possibilities in math most of the time you only want the total number of choices, not the list.

  59. arindameducationusc
    • one year ago
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    ya its working.... thank you....

  60. arindameducationusc
    • one year ago
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    Ok got it! :P

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