Exam 8: A: Advanced Counting Techniques

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

(Short Answer)

4.8/5

(40)

Question 121

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

(Short Answer)

4.7/5

(40)

Question 122

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.

(Short Answer)

4.7/5

(37)

Question 123

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

(Short Answer)

4.8/5

(39)

Question 124

Showing 121 - 124 of 124

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

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

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.

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

The Foundations: Logic and Proofs

A: the Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

A: Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

A: Algorithms

Number Theory and Cryptography

A: Number Theory and Cryptography

Induction and Recursion

A: Induction and Recursion

Counting

A: Counting

Discrete Probability

A: Discrete Probability

Advanced Counting Techniques

Relations

A: Relations

Graphs

A: Graphs

Trees

A: Trees

Boolean Algebra

A: Boolean Algebra

Modeling Computation

A: Modeling Computation

Mathematics Problem Set: Set Theory, Number Theory, Combinatorics, and Boolean Algebra

Filters

Exam 8: A: Advanced Counting Techniques

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

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

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

The Foundations: Logic and Proofs

A: the Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

A: Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

A: Algorithms

Number Theory and Cryptography

A: Number Theory and Cryptography

Induction and Recursion

A: Induction and Recursion

Counting

A: Counting

Discrete Probability

A: Discrete Probability

Advanced Counting Techniques

Relations

A: Relations

Graphs

A: Graphs

Trees

A: Trees

Boolean Algebra

A: Boolean Algebra

Modeling Computation

A: Modeling Computation

Mathematics Problem Set: Set Theory, Number Theory, Combinatorics, and Boolean Algebra

Filters

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

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