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?

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.

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.

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?

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

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!!!!AlexLos 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.GPHesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.JustinKernersville, 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. EstherWoodstock, 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. RobinElkton, 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.DianeDallas, TX