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catgirl17

the kentucky lottery is worth $100,000. to win you have to select the 5 winning numbers from 1-50. how many different combinations are possible?

  • one year ago
  • one year ago

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  1. lgbasallote
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    i believe the formula would be \[\large \frac{50!}{5! 45!}\] feel free to correct me though @apoorvk

    • one year ago
  2. catgirl17
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    where did you get the 45?

    • one year ago
  3. lgbasallote
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    50 - 5 i believe

    • one year ago
  4. ParthKohli
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    Yes, it'd be 50c5 \(\Large \color{purple}{ 50! \over (50 - 5)!*5! }\)

    • one year ago
  5. ParthKohli
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    Get it?

    • one year ago
  6. amorfide
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    |dw:1337518895638:dw|

    • one year ago
  7. ParthKohli
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    nCr is represented as: \(\Large \color{purple}{ {n! \over (n - r)!*r!} }\)

    • one year ago
  8. amorfide
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    n= the amount of numbers =50 r= the numbers you want so 5 50!/(50-5)!5!

    • one year ago
  9. apoorvk
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    no @lgbasallote I won't need to correct you. For choosing 'r' things out 'n', (arrangement not being considered), no. of possible combinations 'N': \[\large N = ^nC_r = \frac{n!}{r!(n-r)!}\]

    • one year ago
  10. lgbasallote
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    heh i cant believe i got the formula right..i only context clues-ed from amistre's work earlier \m/

    • one year ago
  11. ParthKohli
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    If you have to choose 5 numbers from 50, then it'll be 50 choose 5 aka 50c5

    • one year ago
  12. lgbasallote
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    can you go from there now @catgirl17

    • one year ago
  13. ParthKohli
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    Considering that you know what factorials are lolz

    • one year ago
  14. amorfide
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    oh god please know what factorials are...

    • one year ago
  15. lgbasallote
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    it's gonna be a long post slash night if fno

    • one year ago
  16. ParthKohli
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    \(\Large \color{purple}{ n! = n * (n - 1) * (n - 2) * (n - 3) ........1 }\)

    • one year ago
  17. catgirl17
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    after 50!/45!x5! do i just expand it out

    • one year ago
  18. ParthKohli
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    Just having some fun

    • one year ago
  19. lgbasallote
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    yes you do @catgirl17

    • one year ago
  20. ParthKohli
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    And then you cancel to make it simpler.

    • one year ago
  21. lgbasallote
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    and if i were you get rid of x...you might mistake it for a variable

    • one year ago
  22. catgirl17
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    thank you @lgbasallote

    • one year ago
  23. ParthKohli
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    Use * instead of x lol

    • one year ago
  24. lgbasallote
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    \[\huge \color{maroon}{\mathtt{\text{<tips hat>}}}\]

    • one year ago
  25. ParthKohli
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    * doesn't only represent the thing that twinkles. lol

    • one year ago
  26. lgbasallote
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    or use ( )( ) yeah...they're more subtle

    • one year ago
  27. ParthKohli
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    \(\Large \color{purple}{\mathbb{Still} \text{ doesn't get the medal. xP} }\)

    • one year ago
  28. catgirl17
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    when expanding the 50! out do i have to go all the way to 5! ?

    • one year ago
  29. amorfide
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    50! =50x49x48x47......x1

    • one year ago
  30. ParthKohli
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    wait wait... n! OVER r! = (n - r)!

    • one year ago
  31. amorfide
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    50!/45! cancels out to 50x49x48x47x46 divide that by 5!

    • one year ago
  32. lgbasallote
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    just until 45! it will cancel out anyway... \[\large \frac{50! 49! 48! 47! 46! 45!}{45! 5!}\] see? 45! will just cancel out

    • one year ago
  33. amorfide
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    why have you got all those factorials on top?!

    • one year ago
  34. ParthKohli
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    Are you kdding me? 50! is not 50! * 49!........

    • one year ago
  35. lgbasallote
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    fine get rid of the ! :P

    • one year ago
  36. amorfide
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    |dw:1337519562320:dw|

    • one year ago
  37. lgbasallote
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    i just context clues-ed this topic sheesh

    • one year ago
  38. catgirl17
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    is the answer 50,850,240

    • one year ago
  39. ParthKohli
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    n! What it really is ----> n * (n - 1) * (n - 2).......*1 What I think it is -------> n!!!!!!!!!!!!!!!!!!!

    • one year ago
  40. lgbasallote
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    \[\large \frac{50 \times 49 \times 48 \times 47 \times 46 \times 45!}{45!5!}\] 45! cancels out

    • one year ago
  41. catgirl17
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    okay that's what i did

    • one year ago
  42. amorfide
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    do it as a fraction on your scientific calculator

    • one year ago
  43. amorfide
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    i get 2118760

    • one year ago
  44. ParthKohli
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    \(\Large \color{purple} {{50 * 49 * 48 * 47 * 46 \over 5 * 4 * 3 * 2 } }\)

    • one year ago
  45. ParthKohli
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    You need a calculator for this?!?!

    • one year ago
  46. amorfide
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    i dont need one it is just quicker :P

    • one year ago
  47. lgbasallote
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    2118760 it is

    • one year ago
  48. ParthKohli
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    \(\Large \color{purple}{\mathbb{C}\mathbb{A}LCULATOR }\) FAIL.

    • one year ago
  49. catgirl17
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    how did ya'll get that answer cause im not getting that.

    • one year ago
  50. amorfide
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    catgirl what are you putting into your calculator, tell us exactly

    • one year ago
  51. catgirl17
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    50x49x48x47x46/5

    • one year ago
  52. amorfide
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    no it is not 5 it is 5!

    • one year ago
  53. amorfide
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    5!=5x4x3x2x1

    • one year ago
  54. ParthKohli
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    Lol no! The denominator would be 5 * 4 * 3 * 2

    • one year ago
  55. catgirl17
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    would someone just show me how you got your answer and all the steps to get there, please.

    • one year ago
  56. ParthKohli
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    Just read all the replies again. You'll get what we did

    • one year ago
  57. amorfide
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    |dw:1337520226834:dw|

    • one year ago
  58. amorfide
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    n=50 because the over all amount of numbers you have are 50 numbers r=5 because you want a specific 5 from the 50 numbers you have combination means the order of numbers do not matter aslong as you have the numbers there they count as a combination (different to permutations) so the formula is n!/(n-r)!r! sub in

    • one year ago
  59. amorfide
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    ! means it is a factorial and a factorial is the number multiplied by every number before it

    • one year ago
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