## anonymous one year ago How many ways can a teacher arrange four students in the front row with a total of 30 students?

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1. anonymous

I'm confused

2. anonymous

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

3. anonymous

Idk

4. anonymous

Permutation?

5. anonymous

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

6. anonymous

Yes?

7. 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?

8. anonymous

No

9. 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?

10. anonymous

Permutation?

11. 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?

12. anonymous

No

13. 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?

14. anonymous

No

15. anonymous

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

16. anonymous

30

17. anonymous

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

18. anonymous

4

19. 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?

20. anonymous

Not really

21. anonymous

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

22. anonymous

4!x26! ?

23. anonymous

Yes

24. anonymous

I'm using a scientific calculator

25. 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?

26. anonymous

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

27. anonymous

Still there?

28. anonymous

Yes sorry had to do something

29. anonymous

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