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 = 4060For each combination there are 3*2*1 = 6 possible orderings So the total number of different gold, silver, bronze orderings is4060*6 = 24,360Or, 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?
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