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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probability of coloring a $3\times 3$ table with two colors such that no $2\times 2$ square exists
imagine we have a $3\times3$ table ( or $3\times3$ square ) and we want to color each place of that $9$ places with two colors ( red and blue ).
find the probability that no $2\times2$ square exists after coloring places .
Arman Malekzadeh
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Task using principle of inclusions and exclusions.
Let $A = \{ 1,.....,100000\}$. Using principle of inclusions and exclusions determine cardinality $B$.
Let $B$ be such subset $A$ that $e \in B \iff e $ is a number which contains at least one digit from $\{ 3,6,9\}$
I have a problem with counting…
user180834
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No of distinct combinations of non distinct elements
Example:
Given that there are $5$ places that has to be filled with distinct values,, they come from $5$ different bags that contains distinct elements viz $\{1,2,3,5\} ,\{1,2,4\},\{1,3,5\},\{2,3\},\{2\}$
(each bag contain distinct element…
Sidch95
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Distributing different toys
Find the number of ways in which 12 different toys may be distributed among 4 children so that each child gets at least 2 toy.
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How many numbers between 1 and 900 cannot be divided by 4, 5 or 6
I'm trying to find total amount of numbers between 1 and 900 that is not dividable by 4, 5 or 6. For example, number 16 is not part of the total because 16 is dividable with 4. I use inclusion and exclusion and was told the answer is 480. However,…
user333750
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inclusion exclusion proof
there is a step in this proof for the Principle of inclusion-exclusion that is not so clear to me:
\begin{multline*}
|A_1 \cup A_2 \cup \cdots \cup A_n| = \sum_{1 \leq i \leq n} |A_i| - \sum_{1 \leq i < j \leq n} |A_i \cap A_j| \\ + \sum_{1 \leq i <…
PwNzDust
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I have no idea how to solve this question about the principle of inclusion and exclusion. Could anybody help?
How many natural numbers are smaller than $2^{30}$ that are not perfect squares, and not perfect cubes, and not fifth perfect powers?
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How to apply the inclusion exclusion principle
How can I apply the inclusion exclusion principle when I have
$$|Q|+|P|+|R|-|Q\cup P| -|Q\cup R|-|P\cup R|+|Q\cap P\cap R|$$
I'm not sure how to convert the unions into intersections here $$"|Q\cup P| -|Q\cup R|-|P\cup R|"$$ so that I can apply the…
Kaia Zhai
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Inclusion-exclusion principle question - 3 variables
There are 3 types of pants on sale in a store, A, B and C respectively. 45% of the customers bought pants A, 35% percent bought pants B, 30% bought pants C. 10% bought both pants A & B, 8% bought both pants A & C, 5% bought both pants B & C and 3%…
Moonshine45
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Inclusions - Exclusions with areas
Having problems solving this question:
Three carpets, each having an area of $3m^2$, are covering a $6m^2$ section of the floor.
Show that some two carpets overlap on at least $1m^2$ of the floor
Any help tackling this problem would help.
Thank you
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How to apply inclusion - exclusion principle
Let W, X, Y, Z be subsets of {1, 2, . . . , 100} such that W ∩X = ∅, W ∩Y = ∅ and X ∩Y = ∅. Use the inclusion-exclusion principle to write down an expression for |W ∪ X ∪ Y ∪ Z|
Based on the question, I'm puzzled on what Z is as it is not mentioned…
Andrea
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Letters and Envelops problem
Consider a machine whose job is to place 100 letters into 100 envelops.The machine is defective and makes mistakes.What is the probability that in a group of 100 letters no letter is put into the correct envelope?
I did like this.
Total ways of…
user3767495
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Three people take a series of exams, three grades given for each exam. Who placed second in Geometry?
Alice, Betty, and Carol took the same series of examinations. For
each examination there was one mark (grade) of $x$, one mark of $y$, and
one mark of $z$; where $x, y, z$ are distinct positive integers. After all the
examinations, Alice had a total…
Ludwigthestud
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Find the number of permutations of the 8 letters AABBCCDD, taken all at a time, such that no two adjacent letters are alike.
This appears to be an inclusion/exclusion problem. My first step was to find the total permutations with no restrictions, using $\frac{8!}{2!2!2!2!} = 2520$.
What would be the permutation formulas for all adjacent A's, B's, C's, and D's?…
Ludwigthestud
- 195
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Inclusion-Exclusion Principle - Problem
There was a question in my exam discrete maths that I just couldn't figure out. I know it's supposed to be solved using the inclusion-exclusion principle. anyone able to help me solve and understand this question.
For a survey, 200 people are asked…
