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.
Questions tagged [inclusion-exclusion]
1500 questions
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How to find how many students passed both exams?
Here is my question
In a class which has $36$ students, there are $26$ students who passed
math and $20$ students who passed physics exam and $4$ students
couldn't pass the both subjects.
Then, how do we find the students who passed the both…
user440404
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Why does finding the union of these three sets yield a negative number?
I've been working on a homework problem that I can't seem to be able to solve.
The question states:
Suppose 25 people attended a conference that contains 3 sessions. 15 people attended session #1; 18 people attended session #2; 12 people attended…
user486320
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Confused - Inclusion exclusion principle
Hello to everyone who sees this question..
I have seen a problem and it was looking very easy so I tried to solve it but something seems to go wrong..
If there are 3 sets A, B, and C where |A ∪ B ∪ C| = 34, |C ∩ B ∩ A| = 2,
|A ∩ B| = 4, |A ∩ C| =…
Math Newbie
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Cardinality of union of 3 sets
I know there are answers to this specific question, but I'm trying to solve it through a specific line of thought which was used in a textbook on modern algebra for the case with 2 sets. It goes like this:
For two finite sets, let $A'$ and $B'$ be…
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Probability that none of the original pairs are matched (exclusion-inclusion principle)
There are five top hats and five gentlemen. If the five gentlemen pool their top hats and redistribute them at random, what is the probability that none of the gentlemen would have his original top hat?
My original attempt was to directly…
Astaboom
- 957
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Principle of Inclusion and Exclusion Question
54 people were polled about their vacationing habits.
25 vacationed in western Canada,
31 vacationed in central Canada,
28 vacationed in eastern Canada,
11 vacationed in eastern and western Canada,
10 vacationed in eastern and central Canada,
17…
user164403
- 939
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Number of Girls
There are $36$ girls in a class. $19$ of the girls have dark hair and $22$ of them have blue eyes. How many girls have both dark hair and blue eyes?
My attempt was this: Let $d_w$ be girls with dark hair without blue eyes, $d_b$ be girls with dark…
underop
- 3
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Exclusion-inclusion principle- task.
How many such numbers in 5-digit decimal expansion such that:
(1) 3rd digit is 7 and digit 5 there is neither time or
(2) there is no number more than once.
My solution:
Let a set $A$ is a set of numbers satisfying (1),
Let a set $B$ is a set of…
user180834
- 1,453
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Principle of Inclusion and Exclusion Notation
Let $A,B,$ and $C$ be sets such that
$A\subset C, B\subset C$, with $|C|=n$, $|A|=x$, $|B|=y$, and $|A\cap B|=z$.
What is $|C\setminus(A\cup B)|$?
starsaber99
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