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Pulsified333

  • one year ago

For this problem, assume 9 males audition, one of them being George, 6 females audition, one of them being Jackie, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available. How many different ways can these roles be filled if exactly one of George and Jackie gets a part?

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  1. Pulsified333
    • one year ago
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    @jim_thompson5910 @satellite73 @dan815

  2. jim_thompson5910
    • one year ago
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    `if exactly one of George and Jackie gets a part` so they mean just one of them? either George OR Jackie? The wording they have is a bit odd

  3. Pulsified333
    • one year ago
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    yes, i know the wording is odd

  4. jim_thompson5910
    • one year ago
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    I'm going to assume they meant to say George OR Jackie (exactly one person) gets the role. So it's not possible for both to get the role

  5. jim_thompson5910
    • one year ago
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    `9 males audition` `3 male roles available` Let's say George is locked in to get a role. So we really have 3-1 = 2 slots left for the male roles. This is from a pool of 9-1 = 8 males how many ways are there to fill 2 slots from a pool of 8 males?

  6. Pulsified333
    • one year ago
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    ok

  7. Pulsified333
    • one year ago
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    56

  8. jim_thompson5910
    • one year ago
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    order doesn't matter. So you divide 56 by 2 to get 28

  9. Pulsified333
    • one year ago
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    okay but isnt it possible to have any of the three roles

  10. jim_thompson5910
    • one year ago
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    I guess it depends on what the roles are. Are they important roles or extras? Hmm I'm not sure

  11. jim_thompson5910
    • one year ago
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    if the roles are important (eg: leading roles), then order would matter since the characters are different

  12. Pulsified333
    • one year ago
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    so then how do we account for the three roles he could play

  13. jim_thompson5910
    • one year ago
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    I'm not sure now because I'm not sure what the roles are. So I don't know if order matters or not

  14. jim_thompson5910
    • one year ago
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    Sorry I'm not really helpful with this one

  15. Pulsified333
    • one year ago
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    well i have 4 attempts so lets do it with three separate roles on this

  16. jim_thompson5910
    • one year ago
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    ok well if order did matter, then George could have male role A, male role B, male role C he has 3 choices if he picks male role A, then there are 8*7 = 56 ways to fill up the other 2 male roles if he picks male role B, then there are 8*7 = 56 ways to fill up the other 2 male roles if he picks male role C, then there are 8*7 = 56 ways to fill up the other 2 male roles as a shortcut, there are 3*56 = 168 ways to fill up the male roles assuming George gets a male role and order matters (the roles are important roles)

  17. Pulsified333
    • one year ago
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    ok

  18. jim_thompson5910
    • one year ago
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    how many ways are there to fill the female role? We're still under the assumption George got the role. So Jackie can't get the role if George did.

  19. Pulsified333
    • one year ago
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    there is only 1 way if jackie gets the role

  20. jim_thompson5910
    • one year ago
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    like I said ` We're still under the assumption George got the role. So Jackie can't get the role if George did.`

  21. Pulsified333
    • one year ago
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    so what would the answer be

  22. Pulsified333
    • one year ago
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    168?

  23. jim_thompson5910
    • one year ago
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    we're not there yet how many ways are there to fill the female role? assume that Jackie can't get the role

  24. Pulsified333
    • one year ago
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    6

  25. jim_thompson5910
    • one year ago
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    jackie can't get the role though 6-1 = 5 so it's 5 actually

  26. Pulsified333
    • one year ago
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    ah that makes sense

  27. jim_thompson5910
    • one year ago
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    ` 5 children audition` `2 child roles available.` how many ways to fill up these slots?

  28. Pulsified333
    • one year ago
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    20

  29. jim_thompson5910
    • one year ago
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    good

  30. Pulsified333
    • one year ago
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    168*5*20 = 16800

  31. jim_thompson5910
    • one year ago
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    summary so far IF george gets a role, then there are... 168 ways to fill up the male roles 5 ways to fill up the female role 20 ways to fill up the child roles

  32. jim_thompson5910
    • one year ago
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    yes you beat me to it, you multiply those values out

  33. jim_thompson5910
    • one year ago
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    that's just half the answer though

  34. Pulsified333
    • one year ago
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    oh

  35. jim_thompson5910
    • one year ago
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    we haven't considered the scenario that Jackie gets the role

  36. jim_thompson5910
    • one year ago
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    give it a shot and tell me what you get

  37. Pulsified333
    • one year ago
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    10080 if jackie gets the role

  38. Pulsified333
    • one year ago
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    do we subtract them or add them together?

  39. jim_thompson5910
    • one year ago
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    once again, if either Jackie or George gets the role, then the other person can't get it so we're now assuming Jackie gets the role. So george did NOT get the role. Try again

  40. jim_thompson5910
    • one year ago
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    if george did NOT get the role, then the pool of 9 males drops to 8

  41. Pulsified333
    • one year ago
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    sorry 6720

  42. jim_thompson5910
    • one year ago
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    better

  43. jim_thompson5910
    • one year ago
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    we have 2 cases George gets the role: 16800 different ways Jackie gets the role: 6720 different ways add them up

  44. Pulsified333
    • one year ago
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    okay so that is 23520

  45. jim_thompson5910
    • one year ago
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    yes

  46. jim_thompson5910
    • one year ago
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    which is the final answer. It's the number of ways to pick all of the cast based on those specific conditions

  47. Pulsified333
    • one year ago
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    it was the correct answer

  48. Pulsified333
    • one year ago
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    :D

  49. Pulsified333
    • one year ago
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    thanks man

  50. jim_thompson5910
    • one year ago
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    ok so it was a lucky guess on our part to assume order mattered

  51. jim_thompson5910
    • one year ago
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    no problem

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