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catgirl17

  • 2 years ago

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?

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

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

  3. lgbasallote
    • 2 years ago
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    50 - 5 i believe

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

  5. ParthKohli
    • 2 years ago
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    Get it?

  6. amorfide
    • 2 years ago
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    |dw:1337518895638:dw|

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

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

  9. apoorvk
    • 2 years ago
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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': \[\large N = ^nC_r = \frac{n!}{r!(n-r)!}\]

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

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

  12. lgbasallote
    • 2 years ago
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    can you go from there now @catgirl17

  13. ParthKohli
    • 2 years ago
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    Considering that you know what factorials are lolz

  14. amorfide
    • 2 years ago
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    oh god please know what factorials are...

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

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

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

  18. ParthKohli
    • 2 years ago
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    Just having some fun

  19. lgbasallote
    • 2 years ago
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    yes you do @catgirl17

  20. ParthKohli
    • 2 years ago
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    And then you cancel to make it simpler.

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

  22. catgirl17
    • 2 years ago
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    thank you @lgbasallote

  23. ParthKohli
    • 2 years ago
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    Use * instead of x lol

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

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

  26. lgbasallote
    • 2 years ago
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    or use ( )( ) yeah...they're more subtle

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

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

  29. amorfide
    • 2 years ago
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    50! =50x49x48x47......x1

  30. ParthKohli
    • 2 years ago
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    wait wait... n! OVER r! = (n - r)!

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

  32. lgbasallote
    • 2 years ago
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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

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

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

  35. lgbasallote
    • 2 years ago
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    fine get rid of the ! :P

  36. amorfide
    • 2 years ago
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    |dw:1337519562320:dw|

  37. lgbasallote
    • 2 years ago
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    i just context clues-ed this topic sheesh

  38. catgirl17
    • 2 years ago
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    is the answer 50,850,240

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

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

  41. catgirl17
    • 2 years ago
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    okay that's what i did

  42. amorfide
    • 2 years ago
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    do it as a fraction on your scientific calculator

  43. amorfide
    • 2 years ago
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    i get 2118760

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

  45. ParthKohli
    • 2 years ago
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    You need a calculator for this?!?!

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

  47. lgbasallote
    • 2 years ago
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    2118760 it is

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

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

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

  51. catgirl17
    • 2 years ago
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    50x49x48x47x46/5

  52. amorfide
    • 2 years ago
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    no it is not 5 it is 5!

  53. amorfide
    • 2 years ago
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    5!=5x4x3x2x1

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

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

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

  57. amorfide
    • 2 years ago
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    |dw:1337520226834:dw|

  58. amorfide
    • 2 years ago
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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

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

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