zepdrix
  • zepdrix
Combinatorics Question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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zepdrix
  • zepdrix
Eight 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
  • zepdrix
This 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
  • zepdrix
So one way to do it, this ways makes more sense to me... Choose the first and second place people, so this would be 2-permutations 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.

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zepdrix
  • zepdrix
The 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 2-permutations of the 5 we selected to place in first and second? Is that making sense?
zepdrix
  • zepdrix
Ya 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
  • Nnesha
lol' who are you talking to Mr.ghost?

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