How JustAnswer Works:

  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.

Ask dhouse1940 Your Own Question

dhouse1940
dhouse1940, Master's Degree
Category: Math Homework
Satisfied Customers: 676
Experience:  BS mathematics, MS biostatistics, 35+ yrs designing & analyzing biological experiments.
Type Your Math Homework Question Here...
dhouse1940 is online now
A new question is answered every 9 seconds

How many different ways can 30 runners place in an Olympic

Customer Question

How many different ways can 30 runners place in an Olympic qualifying marathon?
Submitted: 2 years ago.
Category: Math Homework
Expert:  Sandhya_sharma replied 2 years ago.
Hi,

Welcome to Justanswer!

How many different ways can 30 runners place in an Olympic qualifying marathon?

Solution:

There are 30 choices for first runner, then 29 for second and then so on

Number of ways = 30*29*28....*1(upto 1) = 30!

Answer: 30!

Please don't forget to click ACCEPT. BONUS is always appreciated.
Customer: replied 2 years ago.
But how would you right that out in a numerical answer.... also how would you determine the different ways three medalists (gold, silver, and bronze) can be chosen from the whole field of 30 runners?
Expert:  Chirag replied 2 years ago.
Hi, can you please post the complete question? Will the fastest 8 runners qualify for the olympics? And you want to find the number of ways the 3 winners can be selected? Please clarify.
Expert:  dhouse1940 replied 2 years ago.
30! is correct and the actual number is XXXXX given because it is huge and tedious to compute. The answer is 30! = 30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*4*3*2*1

The different combinations of 3 medalists from 30 runners is

nCx = n! / [x!*(n – x)!] where a! = a*(a–1)*(a–2)*…*1. So,
30! / [3!*27!] = 30*29*28*27! /(3!*27!) = 30*29*28/ 3!
= 5*29*28 = 4060
For each combination there are 3*2*1 = 6 possible orderings
So the total number of different gold, silver, bronze orderings is
4060*6 = 24,360
Or, simply 30*29*28 = 24,360

If no questions please click on ACCEPT. Bonus is appreciated. Thanks for using JustAnswer.


Customer: replied 2 years ago.

Just to make sure I understand the difference between permutation and combination. You would use the equation for a permutation to establish gold, silver, and bronze because order does matter. However, if you were going to establish the top eight fastest runners, you would use the cobination formula because the top eight will always be the top eight and order would not matter. Correct?

 

So if I were going to determine the number of different ways the eight fastest runners could be chosen from the field of 30, my formula to work out would be 30!/8!22! - which breaks down to 5,852,925 ways, correct?

 

Is there a way to tip more for the answer since you are helping me not only with the answer but understanding it?

Expert:  dhouse1940 replied 2 years ago.
Yes to first question.
Yes to second question (I checked math)

Thanks, XXXXX XXXXX leave a bonus and it would be appreciated.
dhouse1940, Master's Degree
Category: Math Homework
Satisfied Customers: 676
Experience: BS mathematics, MS biostatistics, 35+ yrs designing & analyzing biological experiments.
dhouse1940 and 2 other Math Homework Specialists are ready to help you

JustAnswer in the News:

 
 
 
Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.
 
 
 

What Customers are Saying:

 
 
 
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
< Last | Next >
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
  • This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!! Alex Los Angeles, CA
  • Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult. GP Hesperia, CA
  • I couldn't be more satisfied! This is the site I will always come to when I need a second opinion. Justin Kernersville, NC
  • Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. Esther Woodstock, NY
  • Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. Robin Elkton, Maryland
  • He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here. Diane Dallas, TX
 
 
 

Meet The Experts:

 
 
 
  • Mr. Gregory White

    Master's Degree

    Satisfied Customers:

    85
    M.A., M.S. Education / Educational Administration
< Last | Next >
  • http://ww2.justanswer.com/uploads/ED/educatortech/2012-6-7_1256_williams4.64x64.jpg Mr. Gregory White's Avatar

    Mr. Gregory White

    Master's Degree

    Satisfied Customers:

    85
    M.A., M.S. Education / Educational Administration
  • http://ww2.justanswer.com/uploads/CO/CosumelEyes/2012-5-4_4923_Profile.64x64.jpg Ray Atkinson's Avatar

    Ray Atkinson

    Bachelor's Degree

    Satisfied Customers:

    55
    Grad student. Years and years of tutoring. Education, accounting, and math degrees.
  • http://ww2.justanswer.com/uploads/SO/sonofGauss/2012-6-6_20151_PortraitLHW.64x64.jpg JACUSTOMER-yrynbdjl-'s Avatar

    JACUSTOMER-yrynbdjl-

    Master's Degree

    Satisfied Customers:

    49
    I have taught college Mathematics for the past 10 years.
  • http://ww2.justanswer.com/uploads/homeworklady/2008-11-24_125231_susannewavatar.jpg SusanAthena's Avatar

    SusanAthena

    Master's Degree

    Satisfied Customers:

    38
    Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
  • http://ww2.justanswer.com/uploads/mhasan420/2010-1-23_19189_topi.jpg mhasan420's Avatar

    mhasan420

    Master's Degree

    Satisfied Customers:

    29
    BA Maths, Oxford
  • http://ww2.justanswer.com/uploads/AR/arubin9/2012-2-4_42617_ArthurRubinedit.64x64.jpg Dr Arthur Rubin's Avatar

    Dr Arthur Rubin

    Doctoral Degree

    Satisfied Customers:

    28
    Ph.D. in Mathematics, California Institute of Technology
  • http://ww2.justanswer.com/uploads/DO/Donbacongamer/2012-3-6_2337_mathmaster.64x64.jpg Don's Avatar

    Don

    Master's Degree

    Satisfied Customers:

    17
    M.S. Astronautical Engineering. Math/Science/Comp Tutor
 
 
 

Related Math Homework Questions