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An election ballot asked voters to select three city commissioners from a group of six candidates. In how many ways can this be done?...

Question

An election ballot asked voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

an election ballot asked voters to select three city commissioners from a group of six candidates. In how many ways can this be done?


Answers

Four students are running in an election for class representative on the student council. In how many different ways can the four names be listed on the ballot?

We have to use nations. The election followed us. What us To select three City commission. A group of six. Where'd you hear that? So we are going to fight. Let's support us. So one city commissioners Bravo six. So six bye bye for Rio. Yeah. So their race.

Nations. So the combination that we're doing right now is going to look like this. So that's kind of equal six. No story Okay. Is equal to listen. Yeah, Yeah, yeah. Right? Which is equal to 1 20/6, Which is equal to 20 Yeah.

I have six coordinators you have discovered in how many ways we can organize them on the on this. Oh, on this board, the we're making, um so these should right away tell you I'm gonna per mute them because I want to see how many ways I can organize something How many permutations I can make off something. So that also should tell you factory in number. So I have six of them, so I'm gonna make it factory on six Factory. But again, let's go through the idea. Why staff? So for the first place in which we are trying to place them, we have six options for the second place. Once we fix, the 1st 1 will have only five options. If we fix those two for the third place, we're gonna have only four options. If you fix those three for the fourth place, we're gonna have three options. And if we feed stores four for the 5th 1 we're gonna have only two options, and the 6th 1 is gonna be bound to be the one that is left. So we have in total six times, five times forthe it's three times two times one options, and that's six factorial. That is 720

So there is an election for a class rep And there are four candidates among as the students And of those four candidates available. We want to know in how many ways. So I want to find how many ways can right the four students names up here on and galloped. So I want to find in how many ways Can we list those four names on a ballot paper? Uh So basically um let's just call the students to be A, B, C. And D. Alright, so to put the name in the first position, There are four ways of putting all the names in the first position. But once the name has been put, There are three names left now. Um And when the second is placed We are left with two names and when the third displaced Only one is left. So these are the number of ways in which four names can be written on the ballot box. So that's four times three, 12 times two, So basically this is just for victoria ways Which is 24. So their 24 ways.


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