anonymous
  • anonymous
How many ways can a teacher arrange four students in the front row with a total of 30 students?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I'm confused
anonymous
  • anonymous
Is this a combination or a permutation? What do you think?
anonymous
  • anonymous
Idk

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anonymous
  • anonymous
Permutation?
anonymous
  • anonymous
Does the order in which the four students placed in the front row matter?
anonymous
  • anonymous
Yes?
anonymous
  • 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
  • anonymous
No
anonymous
  • 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
  • anonymous
Permutation?
anonymous
  • 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
  • anonymous
No
anonymous
  • 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
  • anonymous
No
anonymous
  • anonymous
OK. In this question, n is the total number of people. How many is that?
anonymous
  • anonymous
30
anonymous
  • anonymous
Yup. And r is the number of people that are chosen to sit in the front row. How many is that?
anonymous
  • anonymous
4
anonymous
  • 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
  • anonymous
Not really
anonymous
  • anonymous
Do you know what the factorial symbol (!) means?
anonymous
  • anonymous
4!x26! ?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
I'm using a scientific calculator
anonymous
  • 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
  • anonymous
If so, there are a lot of common factors in the numerator and denominator that cancel out.
anonymous
  • anonymous
Still there?
anonymous
  • anonymous
Yes sorry had to do something
anonymous
  • anonymous
Cancel out the common factors and calculate the result. What do you get?

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