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# combinatorics question watch

1. Suppose that m 0s and n 1s are arranged in random order, with each possible arrangement being equally likely. Show that the probability that the resulting sequence is 0-dominated is 1 - n/(m+1).
2. (Original post by Fringe_Agent13)
..
I assume you're working from "Combinatorics: A Problem Oriented Approach" (I'd never heard the term 0-dominated before and had to google it). (If not, use google to find the pages from that book).

Use the same argument as in B27 to find the number of sequences that are NOT 0 dominated. From there it's a couple of (easy) lines of manipulation.

Post again if you're stuck.
3. (Original post by DFranklin)
I assume you're working from "Combinatorics: A Problem Oriented Approach" (I'd never heard the term 0-dominated before and had to google it). (If not, use google to find the pages from that book).

Use the same argument as in B27 to find the number of sequences that are NOT 0 dominated. From there it's a couple of (easy) lines of manipulation.

Post again if you're stuck.
Couldn't I just permute the 0s and 1s and use the algorithm, found right after B27, to find the number of 0-dominated sequences. Then, divide the number of 0-dominated sequences by the permutation?
4. (Original post by Fringe_Agent13)
Couldn't I just permute the 0s and 1s and use the algorithm, found right after B27, to find the number of 0-dominated sequences. Then, divide the number of 0-dominated sequences by the permutation?
Yes, that's what I said.
5. (Original post by DFranklin)
Yes, that's what I said.
What do you personally call a "dominated sequence?" I try and look up more info. on them and nothing comes up. I don't think that's a common name.
6. (Original post by Fringe_Agent13)
What do you personally call a "dominated sequence?" I try and look up more info. on them and nothing comes up. I don't think that's a common name.
I had to Google it - I'd never heard the term.

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