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anonymous
 one year ago
How many ways can a teacher arrange four students in the front row with a total of 30 students?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is this a combination or a permutation? What do you think?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does the order in which the four students placed in the front row matter?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 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
 one year ago
Best ResponseYou've already chosen the best response.0Great. 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
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, 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
 one year ago
Best ResponseYou've already chosen the best response.0The number of combinations of choosing r items out of a set on n items is given by\[_{n}C _{r}=\frac{ n! }{ r!\left( nr \right)! }\]Do you understand this equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. In this question, n is the total number of people. How many is that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup. And r is the number of people that are chosen to sit in the front row. How many is that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right. So the calculation becomes\[_{30}C _{4}=\frac{ 30! }{ 4!\left( 304 \right)! }=\frac{ 30! }{ 4!26! }\] Can you calculate this answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what the factorial symbol (!) means?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm using a scientific calculator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great. 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
 one year ago
Best ResponseYou've already chosen the best response.0If so, there are a lot of common factors in the numerator and denominator that cancel out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes sorry had to do something

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cancel out the common factors and calculate the result. What do you get?
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