## zepdrix one year ago Combinatorics Question

1. 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?

2. 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.

3. 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.

4. 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?

5. 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

6. Nnesha

lol' who are you talking to Mr.ghost?