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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{A squad consists of 16 cricketers including Sachin and Rahul. }\hspace{.33em}\\~\\ & \normalsize \text{ In how many ways can the team of 11 cricketers be selected such that,}\hspace{.33em}\\~\\ & \normalsize \text{If Sachin is selected then Rahul is dropped and }\hspace{.33em}\\~\\ & \normalsize \text{if Rahul is selected then Sachin is dropped .}\hspace{.33em}\\~\\ \end{align}}\)

  2. mathmath333
    • one year ago
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    @amilapsn

  3. amilapsn
    • one year ago
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    There are three possible kinds of situations can you guess them:

  4. mathmath333
    • one year ago
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    there are 2 possiblities

  5. amilapsn
    • one year ago
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    Question can be interpreted in many ways... ok.. tell me what your two possibilities are...

  6. mathmath333
    • one year ago
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    Is S is there R is not vice versa

  7. mathstudent55
    • one year ago
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    Since you can only make a team without one or without the other or without both, think of making a team of 11 out of 15 (no Sachin) and a team of 11 out of 15 (no Rahul).

  8. amilapsn
    • one year ago
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    then what about both of them are not in the team?

  9. ganeshie8
    • one year ago
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    isn't the answer simply \[\binom{16}{11} - \binom{14}{11}\]

  10. mathstudent55
    • one year ago
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    \(2(_{15}C_{11})\)

  11. amilapsn
    • one year ago
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    @ganeshie8 yes indeed that's another way of doing it...

  12. amilapsn
    • one year ago
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    It's much simpler than my method...:)

  13. amilapsn
    • one year ago
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    @mathmath333 did you get ganeshie's one?

  14. mathmath333
    • one year ago
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    u mean this one \(\Large \dbinom{16}{11} - \dbinom{14}{9}\)

  15. mathmath333
    • one year ago
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    not really

  16. amilapsn
    • one year ago
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    yep

  17. ganeshie8
    • one year ago
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    it is 14 choose 11 not 14 choose 9

  18. mathmath333
    • one year ago
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    but in book it is given this \(\Large \dbinom{16}{11} - \dbinom{14}{9}\)

  19. mathmath333
    • one year ago
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    any way i didn't get how that comes

  20. amilapsn
    • one year ago
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    it is \(\color{red}{16}\) choose 11 not 14 choose 9

  21. mathmath333
    • one year ago
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    ok but how did u get this answer \(\dbinom{16}{11} - \dbinom{14}{11}\)

  22. amilapsn
    • one year ago
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    \( \dbinom{16}{11}\) means number of all teams that can be made without considering the condition.. ok?

  23. mathmath333
    • one year ago
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    yes

  24. amilapsn
    • one year ago
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    Then we just have to remove the number of teams where there are S and R both , right?

  25. ganeshie8
    • one year ago
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    Ahh right, @amilapsn thanks for catching :)

  26. mathmath333
    • one year ago
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    ok

  27. amilapsn
    • one year ago
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    Then we are left with: 1.teams where there is not S or R 2.teams with only S 3 teams with only R Condition fulfilled...

  28. mathmath333
    • one year ago
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    Then we just have to remove the number of teams where there are S and R both this will be done by \(-\dbinom{14}{11}\) ?

  29. amilapsn
    • one year ago
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    Yes. Because We've already chosen dravid and thendulkar so we only have to choose anothe nine players out of the rest(14).. Got that?

  30. mathmath333
    • one year ago
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    and by other method can u tell me 1.teams where there is not S or R 2.teams with only S 3 teams with only R

  31. amilapsn
    • one year ago
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    1-we've choose 11 out of 14 2-we've already chosen S so we have to make sure that R is no there so now we have to choose 10 out of 12 3-the same as 2 we've to choose 10 out of 12

  32. mathmath333
    • one year ago
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    2-we've already chosen S so we have to make sure that R is no there so now we have to choose 10 out of \(\color{red}{12}\) 3-the same as 2 we've to choose 10 out of \(\color{red}{12}\) how does \(\color{red}{12}\) comes

  33. amilapsn
    • one year ago
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    Let's consider the second situation... After choosing S how much players we are left with?

  34. mathmath333
    • one year ago
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    15

  35. amilapsn
    • one year ago
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    then can we get R to the team?

  36. mathmath333
    • one year ago
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    no

  37. amilapsn
    • one year ago
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    Then how much we've to consider?

  38. mathmath333
    • one year ago
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    14

  39. amilapsn
    • one year ago
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    So we've to choose 10 out of 14... (omg my bad that 12 should be 14... sorry for that mistake)

  40. amilapsn
    • one year ago
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    wait a sec... Let me see...

  41. amilapsn
    • one year ago
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    Ok so what's the problem? We are alright, know?

  42. mathmath333
    • one year ago
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    \(\dbinom{16}{11}-\dbinom{14}{11}\) u said earlier that this is correct but wolfram isn't matching it with the other way

  43. amilapsn
    • one year ago
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    that second 11 should be nine: I've said that:\[\text{Yes. Because We've already chosen dravid and thendulkar so we only have to choose}\] \[\text{anothe nine players out of the rest(14).. Got that?}\]

  44. mathmath333
    • one year ago
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    ok lol i missed that comment earlier completely thanks

  45. amilapsn
    • one year ago
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    Yw!

  46. ganeshie8
    • one year ago
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    hows the test between india and lanka going

  47. amilapsn
    • one year ago
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    We won the 1st one you know... It was a legendary match due to Chandimal's playing.. Today match is also a very important for all Sri Lankans because it is the final match of Sanga. We'll miss him so much...

  48. mathmath333
    • one year ago
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    In the question why we didn't include the case both sachin and rahul are selected.

  49. amilapsn
    • one year ago
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    Because the it's said in the question:\[\large \color{black}{\begin{align} & \normalsize \text{A squad consists of 16 cricketers including Sachin and Rahul. }\hspace{.33em}\\~\\ & \normalsize \text{ In how many ways can the team of 11 cricketers be selected such that,}\hspace{.33em}\\~\\ & \normalsize \text{If Sachin is selected then Rahul is dropped and }\hspace{.33em}\\~\\ & \normalsize \text{if Rahul is selected then Sachin is dropped .}\hspace{.33em}\\~\\ \end{align}}\]

  50. mathmath333
    • one year ago
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    by the way india lost 1st test against lanka

  51. mathmath333
    • one year ago
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    are u from lanka

  52. amilapsn
    • one year ago
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    yep.

  53. mathmath333
    • one year ago
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    but it was also not stated that both sachin and rahul won't be selected, then also we add it

  54. amilapsn
    • one year ago
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    But it doesn't break the condition right? We have to account for all situations without breaking the condition..

  55. mathmath333
    • one year ago
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    but y it dont break the condition

  56. dan815
    • one year ago
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    TotalWays - Ways of sachin and Rahul

  57. dan815
    • one year ago
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    when you to 16 Choose 11 right now in all those combinations it includes the one where both of them are selected that is the only part we have to subtract

  58. amilapsn
    • one year ago
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    That's the nature of "if". Have you done logic @mathmath333 ?

  59. mathmath333
    • one year ago
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    no

  60. dan815
    • one year ago
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    so 16 Choose 11 - 14 Choose 9

  61. dan815
    • one year ago
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    there are a couple other ways of adding the different cases, this is one way

  62. dan815
    • one year ago
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    another way is to add the cases of no sachin and rahul then only sachin then only rahul

  63. amilapsn
    • one year ago
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    \[\href{ https://en.wikipedia.org/wiki/Material_conditional {\huge p\Rightarrow q}\]

  64. mathmath333
    • one year ago
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    ok thanks i will look at this logic thing and interpretation of "if"

  65. amilapsn
    • one year ago
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    It's pretty simple you'll get it easily.

  66. dan815
    • one year ago
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    2*(14 Choose10) + 14 choose 11 ^ ^________no rahul and sachil '------ only rahul + only sachin also should work

  67. dan815
    • one year ago
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    you can actually go on to show this actually always true 2*(14 Choose10) + 14 choose 11 = 16 choose 11 - 14 choose 9 2*(n choose k) + n choose (k+1) = (n+2) choose (k+1) - n choose(k-1)

  68. dan815
    • one year ago
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    if u like that sorta thing lol.. try proving that

  69. dan815
    • one year ago
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    |dw:1440177672216:dw|

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