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Results tagged with combinatorics
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user 157
Questions related to combinatorics and discrete mathematical structures
3
votes
Accepted
How many possible ways are there?
Say you want to pick, out of a multiset $S$, the numbers $x_1$, $x_2$, ..., $x_n$ with multiplicity $m_1$, $m_2$, ..., $m_n$ (i.e., you want to pick $x_1$ exactly $m_1$ times).
Furthermore, assume th …
- 20.8k
5
votes
Accepted
Distinguishing between uppercase and lowercase letters in the "move-to-front" method
Though for us, human beings, m and M are the same, for a computer these are two distinct symbols that have no relation whatsoever.
The answer actually depends on the application:
If your applicati …
- 20.8k
19
votes
Accepted
Pizza commercial claim of 34 million combinations
Ok, A bit more detailed answer than in the comments.
Choosing $k$ out of $n$ is done by ${n \choose k} = \frac{n!}{k!(n-k)!}$. So for things like the size of the pizza, where you have 4 options (and …
- 20.8k
1
vote
Bound covariance of two discrete random variables
This follows from Pinsker's inequality. The inequality states that for any two distributions (here, discrete) $P$, and $Q$, it holds that
$$\|P-Q\| \le \sqrt{2D_{\text{KL}}(P\|Q)} $$
where $D_{\text{ …
- 20.8k
6
votes
Finding the number of distinct permutations of length N with n different symbols
The total number of (different) permutations of strings with $n_i$ characters of type $i$ is given by
$$\frac{(\sum_i n_i)!}{\prod_i n_i!}.$$
In other words, if the length of the string is $n=n_1 + n_ …
- 20.8k