Question 1

Find $$\left| A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 } \right| \text { if each set } A _ { i }$$ has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

Accepted Answer

The answer of Find \[\left| A _ { 1 }...

Question 2

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

Accepted Answer

\[\left( \begin{arra...

Question 3

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = a _ { n - 1 } + 2 n + 1 , \quad a _ { 0 } = 5$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 4

Use generating functions to solve $$a _ { n } = 3 a _ { n - 1 } + 2 ^ { n } + 5 , a _ { 0 } = 1$$

Accepted Answer

The answer of Use generating functions to solve \[a _...

Exam 8: A: Advanced Counting Techniques

Use generating functions to solve $a _ { n } = 3 a _ { n - 1 } + 2 ^ { n } + 5 , a _ { 0 } = 1$

Correct Answer
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Find $\left| A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 } \right| \text { if each set } A _ { i }$ has 100 elements, each intersection of two sets has 60 elements, each intersection of three sets has 20 elements, and there are 10 elements in all four sets.

Correct Answer
verified

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

Correct Answer
verified
\[\left( \begin{arra...
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solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 1 } + 2 n + 1 , \quad a _ { 0 } = 5$

Correct Answer
verified

Exam 8: A: Advanced Counting Techniques

Use generating functions to solve an=3an−1+2n+5,a0=1a _ { n } = 3 a _ { n - 1 } + 2 ^ { n } + 5 , a _ { 0 } = 1an​=3an−1​+2n+5,a0​=1

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

How many ways are there to choose ﬁve donuts if there are eight varieties and only the type of each donut

Correct Answerverified\[\left( \begin{arra...View AnswerShow Answer

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=an−1+2n+1,a0=5a _ { n } = a _ { n - 1 } + 2 n + 1 , \quad a _ { 0 } = 5an​=an−1​+2n+1,a0​=5

Correct AnswerverifiedShow Answer

Use generating functions to solve $a _ { n } = 3 a _ { n - 1 } + 2 ^ { n } + 5 , a _ { 0 } = 1$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
\[\left( \begin{arra...
View Answer

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 1 } + 2 n + 1 , \quad a _ { 0 } = 5$

Correct Answer
verified