In how many ways can first, second, and third prizes be awarded in a contest with 280 contestants

for this problem we are told about A contest where there are 960 contestants and were asked in part a how many ways can 1st, 2nd and 3rd prizes be awarded. So here we have to select three people Out of 960. And the order matters because their 1st, 2nd and 3rd prizes. So that means that these are permutations. So you may or may not use this this uh notation, but when we have and people to choose from and we are choosing three of them, Number of permutations can be denoted this way and it's equal to n. Factorial divided by n minus R factorial. So here we have And it's 960 and we are picking three contestants. So this is 960 factorial Over 9 57 factorial. And this comes out to you. So I got this right is eight, million. 973,000 120. So this is the total number of ways That 1st, 2nd and 3rd prizes can be awarded. And then for part part B we're asked if we are in if you are in the contest, what is the probability of you placing? So this means what is the probability of you coming in 1st, 2nd or third, if the prizes are decided randomly. So one way to look at this is to not worry about the order whether you get 1st, 2nd or third, all you want to concern yourself with is whether or not you are in the top three. And so we can look at the probability as being the number of ways that you can be in the group of the three people who are awarded prizes, Divided by the total number of ways of selecting a group, a group of three from 960 contestants. So for the numerator, this is the total number of ways that you are in the top three. Without worrying about order. It's one, choose one that represents choosing you. And then if you're in the contest, that means there are 959 other people And we must choose two of them to round out the top three. So this so far represents the total number of ways That you are in the top three. If order is not considered now, the total number of ways of awarding the top three without concerning ourselves with order just selecting three people who will win one of the prizes, It's 960 choose three. And this comes out to .0031 approx. So the probability that you are in the top three if the prizes are awarded randomly is

Srikar K.
Temple University

Catherine R.
Missouri State University

Boris M.
University of North Carolina at Chapel Hill

Megan C.
Piedmont College

Christine G.
Cairn University

Monique R.
Numerade Educator

Heather Z.
Oregon State University

Lucas E.
University of St. Thomas

Michael J.
Idaho State University

Joseph L.
Boston College

Data And Variables

Data And Variables - Example 1

In how many ways can first, s…

In how many ways can first, s…

79 students enter a contest a…

- [ ] 59 students enter a con…