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zepdrix
 one year ago
Combinatorics Question
zepdrix
 one year ago
Combinatorics Question

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Eight people enter a competition. In how many ways can `a first prize`, `a second prize`, `and three identical third prizes` be awarded to these eight people?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1This was a quiz from a previous week. The teacher has since given us the answer, but I think she made a typo. I wanted to see if someone could verify.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So one way to do it, this ways makes more sense to me... Choose the first and second place people, so this would be 2permutations of 8 people. \(\large\rm P(8,2)=\frac{8!}{6!}\) And for the remaining three places, since they're identical, order will not matter, and we're simply looking at combinations of these uhh remaining slots. \(\rm \left(\begin{matrix}6\\3\end{matrix}\right)=\dfrac{6!}{3!3!}\) Answer = 1120.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The other way the teacher showed it... was to do \(\large\rm \left(\begin{matrix}8\\5\end{matrix}\right)P(5,2)=\dfrac{8!}{5!3!}\cdot\dfrac{5!}{3!}\) Hmm this one also equals out to 1120. I can't seem to make sense of it though. So we're ... choose 5 people from 8, not regarding order at this point. And then we're doing 2permutations of the 5 we selected to place in first and second? Is that making sense?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ya maybe I didn't need to open up a question for this one _ shoulda just thought it through lol I think it's making more sense now

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0lol' who are you talking to Mr.ghost?
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