How many ways can a teacher arrange four students in the front row with a total of 30 students?

- anonymous

How many ways can a teacher arrange four students in the front row with a total of 30 students?

- schrodinger

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- anonymous

I'm confused

- anonymous

Is this a combination or a permutation? What do you think?

- anonymous

Idk

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## More answers

- anonymous

Permutation?

- anonymous

Does the order in which the four students placed in the front row matter?

- anonymous

Yes?

- anonymous

So let's say that Bill, Jim, Sue, and Betty are chosen to sit in the front row. Does it matter in what order they sit?

- anonymous

No

- anonymous

Great. So, as long as those four are chosen, it doesn't matter in which order they're chosen. If the order doesn't matter, is that a combination or a permutation?

- anonymous

Permutation?

- anonymous

Sorry, no. If the order doesn't matter, then it's a combination. If the order does matter, then it's a permutation. So this question is about calculating a combination. Do you know how to do that?

- anonymous

No

- anonymous

The number of combinations of choosing r items out of a set on n items is given by\[_{n}C _{r}=\frac{ n! }{ r!\left( n-r \right)! }\]Do you understand this equation?

- anonymous

No

- anonymous

OK. In this question, n is the total number of people. How many is that?

- anonymous

30

- anonymous

Yup. And r is the number of people that are chosen to sit in the front row. How many is that?

- anonymous

4

- anonymous

Right. So the calculation becomes\[_{30}C _{4}=\frac{ 30! }{ 4!\left( 30-4 \right)! }=\frac{ 30! }{ 4!26! }\] Can you calculate this answer?

- anonymous

Not really

- anonymous

Do you know what the factorial symbol (!) means?

- anonymous

4!x26! ?

- anonymous

Yes

- anonymous

I'm using a scientific calculator

- anonymous

Great. So you have\[_{30}C _{4}=\frac{ 30\times29\times28\times27\times26\times25\times24\times...\times2\times1 }{\left( 4\times3\times2\times1 \right)\left( 26\times25\times24\times...\times2\times1 \right) }\]Make sense?

- anonymous

If so, there are a lot of common factors in the numerator and denominator that cancel out.

- anonymous

Still there?

- anonymous

Yes sorry had to do something

- anonymous

Cancel out the common factors and calculate the result. What do you get?

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