Halp with math.

[Chaicho]

Can someone explain this problem to me? What is the formula.

[TidaLWaveZ]

It's a permutation as the order does matter for example the same person can not get first and second place.

 

n is the entire population (10)

r is the subset which is the available prizes(3)

 

permutations = n! / (n - r)!

 

10! / (10-3)!

 

10! / 7! = 720

 

[Chaicho]

9 minutes ago, TidaLWaveZ said:

It's a permutation as the order does matter for example the same person can not get first and second place.

 

n is the entire population (10)

r is the subset which is the available prizes(3)

 

permutations = n! / (n - r)!

 

10! / (10-3)!

 

10! / 7! = 720

 

Thanks!

[pyrojoe34]

@TidaLWaveZ is correct.

The only thing I would add is to make sure you understand the logic behind the equation rather than just the equation. When you break it down it is really easy to answer without it.

 

You have three prizes and 10 people.

1. how many different people can win first prize?

10

 

2. how many people can win second prize?

Since someone has already won the first they cannot also win the second. That means only 9 people can win the second prize.

 

3. how many people can win third prize?

Since one person has already won first and another already won second, there are only 8 people left that can win the third prize.

 

So you have 10 possibilities for first, 9 for second, and 8 for third.

 

10*9*8 = 720 possible combinations.

 

As a logic check: If instead, there are three different contests and only one prize per contest (assuming that the same person could win multiple times) you could use the same logic to deduce that there are 10 options every time. In that case, the answer would be 10*10*10 = 1000 possible combinations.

 

It's very important in math to not just know equations, but to understand equations. The biggest flaw I see in our way of teaching math is that many people rely on memorizing equations rather than understanding them. This is a dangerous way to learn things as it can very easily cause people to make mistakes without realizing it, and more importantly, it limits people's abilities to extrapolate equations on their own. If you gain a fundamental understanding of the math you learn, you will never have to memorize any equations and will start to see math as something that "just makes sense" and comes easily rather than something you have to memorize.

[Chaicho]

8 hours ago, pyrojoe34 said:

@TidaLWaveZ is correct.

The only thing I would add is to make sure you understand the logic behind the equation rather than just the equation. When you break it down it is really easy to answer without it.

 

You have three prizes and 10 people.

1. how many different people can win first prize?

10

 

2. how many people can win second prize?

Since someone has already won the first they cannot also win the second. That means only 9 people can win the second prize.

 

3. how many people can win third prize?

Since one person has already won first and another already won second, there are only 8 people left that can win the third prize.

 

So you have 10 possibilities for first, 9 for second, and 8 for third.

 

10*9*8 = 720 possible combinations.

 

As a logic check: If instead, there are three different contests and only one prize per contest (assuming that the same person could win multiple times) you could use the same logic to deduce that there are 10 options every time. In that case, the answer would be 10*10*10 = 1000 possible combinations.

 

It's very important in math to not just know equations, but to understand equations. The biggest flaw I see in our way of teaching math is that many people rely on memorizing equations rather than understanding them. This is a dangerous way to learn things as it can very easily cause people to make mistakes without realizing it, and more importantly, it limits people's abilities to extrapolate equations on their own. If you gain a fundamental understanding of the math you learn, you will never have to memorize any equations and will start to see math as something that "just makes sense" and comes easily rather than something you have to memorize.

Holy crap that makes it a lot easier. Thanks man.

[Velvet Revolver]

you should spend more time in English class.