The inclusion-exclusion principle states that the number of elements in the union of two given sets is the sum of the number of elements in each set, minus the number of elements that are in both sets.
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Famous uses of the inclusion-exclusion principle?
The standard textbook example of using the inclusion-exclusion principle is for solving the problem of derangement counting; using inclusion-exclusion (and some basic analysis) it can be shown that ...
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2answers
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Using Inclusion-Exclusion on $n$ boys and $n$ girls
Consider a set of n boys and n girls. In each situation below, use inclusion-exclusion to derive formulas for the number of ways to partition the $2n$ people into pairs so that for each $i$ the $i$-th ...
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Combinatorics: Using Inclusion-Exclusion Principle
I'm not sure how to start this. I've been told to use inclusion-exclusion, but I don't know which properties to use.
Intuitively, I want to solve the problem like this:
$E_1$ = 1 person leaves ...
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When to use Inclusion Exclusion principle?
I'm a bit confused as to when you should use the Incl/Excl principle. Take for example the following problem:
How many 13-card hands can be selected from the standard 52-card deck with exactly four ...
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Are the error terms of the partial sums of inclusion-exclusion unimodal?
I often teach inclusion-exclusion: $$|A ∪ B| = |A| + |B| − |A ∩ B|$$
by suggesting that $|A∩B|$ is a correction factor for $|A|+|B|$. Then I teach the three set version:
$$|A∪B∪C| = |A| + |B| + |C| ...
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Number of solutions to an equation using the inclusion-exclusion principle [duplicate]
Possible Duplicate:
Inclusion-exclusion principle: Number of integer solutions to equations
This is a problem that I have had much trouble with. If you attempt in helping me with this, ...
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votes
3answers
2k views
Inclusion-exclusion principle: Number of integer solutions to equations
The problem is:
Find the number of integer solutions to the equation
$$
x_1 + x_2 + x_3 + x_4 = 15
$$
satisfying
$$
\begin{align}
2 \leq &x_1 \leq 4, \\
-2 \leq &x_2 \leq 1, \\
0 \leq ...
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votes
1answer
290 views
A question about the Inclusion-Exclusion principle
Grandma has 8 grandchildren, and 4 different types of popsicles:
6 Vanilla popsicles
6 Strawberry popsicles
5 Banana popsicles
3 Chokolate popsicles
This morning, all of her grandchildren came ...
