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anonymous

  • one year ago

From a deck of 52 cards, how many 5-card hands can be formed with at least 3 diamonds?

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  1. anonymous
    • one year ago
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    there are 13 diamonds divided by 3 gives 4 possible decks with at least 3 diamonds

  2. anonymous
    • one year ago
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    wut.

  3. Zarkon
    • one year ago
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    A lot. What have you tried?

  4. anonymous
    • one year ago
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    im not sure, i feel like it starts off with \[? nCr 5 \]?

  5. Zarkon
    • one year ago
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    do you know how many hands if there are exactly 3 diamonds?

  6. anonymous
    • one year ago
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    :/ no...

  7. anonymous
    • one year ago
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    5 hand?

  8. Zarkon
    • one year ago
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    how many ways can you choose 3 cards from 13?

  9. anonymous
    • one year ago
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    so 13 Cr 3?

  10. anonymous
    • one year ago
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    o wait

  11. anonymous
    • one year ago
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    i meant 13 nCr 3

  12. Zarkon
    • one year ago
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    drop the r \[\Large_{13}C_3\]

  13. Zarkon
    • one year ago
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    ok how many cards are not diamonds?

  14. anonymous
    • one year ago
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    i don't know

  15. Zarkon
    • one year ago
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    a card is a diamond or it is not. you have 52 total cards and 13 of them are diamonds

  16. anonymous
    • one year ago
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    39

  17. Zarkon
    • one year ago
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    ok

  18. Zarkon
    • one year ago
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    how many ways can you choose the remaining 2 card from the 39?

  19. anonymous
    • one year ago
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    38?

  20. anonymous
    • one year ago
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    so 39 * 38 * 37

  21. Zarkon
    • one year ago
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    no

  22. Zarkon
    • one year ago
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    this is again a combination

  23. Zarkon
    • one year ago
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    you are CHOOSING 2 cards from 39

  24. anonymous
    • one year ago
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    what where did the 2 come from

  25. Zarkon
    • one year ago
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    you are picking a 5 card hand. 3 are diamonds...thus the other 2 cards must not be diamonds

  26. anonymous
    • one year ago
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    oh psh right :/

  27. anonymous
    • one year ago
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    um so after 2, 37's left

  28. Zarkon
    • one year ago
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    I don't care how many are left after you pick 2. We need to know how many ways we can pick the 2 cards from the 39

  29. Zarkon
    • one year ago
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    it is the same exact idea we used to choose the 3 diamonds

  30. anonymous
    • one year ago
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    39 C 2

  31. anonymous
    • one year ago
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    and then multiply it with 13 C 3

  32. Zarkon
    • one year ago
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    yes

  33. Zarkon
    • one year ago
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    but that is not the final answer

  34. Zarkon
    • one year ago
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    because they are asking for AT LEAST 3 diamonds we need to do this tow more times. one with 4 diamonds and one with 5 diamonds

  35. Zarkon
    • one year ago
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    *two

  36. Zarkon
    • one year ago
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    N(at least 3 diamonds) =N(get exactly 3 diamonds)+N(get exactly 4 diamonds)+N(get exactly 5 diamonds)

  37. anonymous
    • one year ago
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    13 C 4 * 38 C 1; 13 C 5 * 37 C 0

  38. anonymous
    • one year ago
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    oh

  39. Zarkon
    • one year ago
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    almost

  40. Zarkon
    • one year ago
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    there are always 39 cards that are not diamonds

  41. anonymous
    • one year ago
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    LOL shet

  42. anonymous
    • one year ago
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    ok

  43. anonymous
    • one year ago
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    so it's 13 C 4 * 39 C 1; 13 C 5 * 39 C 0

  44. Zarkon
    • one year ago
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    yes...so what is the final answer?

  45. anonymous
    • one year ago
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    211926?

  46. Zarkon
    • one year ago
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    no

  47. anonymous
    • one year ago
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    oh no

  48. anonymous
    • one year ago
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    crap

  49. anonymous
    • one year ago
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    one sec

  50. anonymous
    • one year ago
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    241098

  51. Zarkon
    • one year ago
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    yes

  52. anonymous
    • one year ago
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    LOL THANK YOU SO MUCH

  53. Zarkon
    • one year ago
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    no problem

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