Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mameadows Group Title

what is the probability that your five number combination will be the winning combination in a lottery that involves the selection of random numbers from 1 through 20? the order of the five numbers is irrelevant.

  • 11 months ago
  • 11 months ago

  • This Question is Closed
  1. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    When order matters, the total number of tickets (sample space) is \(20^5\) We can remove order by dividing out the number of permutations from the sample space. The \(5\) numbers can be permuted \(5!\) ways. Thus I ways say the probability is: \[ \frac {5!}{20^5} \]

    • 11 months ago
  2. mameadows Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @wio can I leave my answer like that or do I have to actually multiply them out?

    • 11 months ago
  3. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You should multiply them out.

    • 11 months ago
  4. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ 5!=5\times4\times3\times2\times 1=20\times 3\times 2 \]

    • 11 months ago
  5. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \frac{20\times 3\times 2}{ 20^5} = \frac{3\times 2}{20^4} = \frac{3}{10^4\times 2^3} \]At this point you may just want to use a calculator.

    • 11 months ago
  6. mameadows Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    this is what i thought it was: 20*19*18*17*16*15! / 15! * 5*4*3*2*1 = 1,860,480 / 120 = 15,504... you can only get one winning ticket so... 1 / 15,504 is that wrong?

    • 11 months ago
  7. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't understand the reasoning behind that so I can't tell you what is wrong with it.

    • 11 months ago
  8. mameadows Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    total no:(1-20)=29 use combination ,u have to select only 5 no's total no of ways=20 C 5 =20! / (15! * 5!) =20*19*18*17*16*15! / (15! * 5*4*3*2*1) =15,504 since only one will be correct out of these ways therefore answer is 1/15,504

    • 11 months ago
  9. mameadows Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I meant to put (1-20)=20! at the top

    • 11 months ago
  10. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, the reason we use \(20^5\) instead of \(20!/15!\) is because it didn't say we can't have repeated numbers.

    • 11 months ago
  11. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It didn't say we can't chose something like 1 1 1 1 1

    • 11 months ago
  12. mameadows Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    got it... thx

    • 11 months ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.