What generating functions can be used to find the number of ways in which postage of...
What generating functions can be used to find the number of ways in which postage of r cents can be pasted on an envelope using 1-cent, 3-cent, and 20-cent stamps?
(a) Assume that the order the stamps are pasted on does not matter.
(b) Assume that the stamps are pasted in a row and their order matters.
Homework Answers
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What generating functions can be used to find the number of ways
in which postage of...
need steps A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number...
need steps
A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number of ways to form postage of n cents if the order of the stamps matters, i.e.. different orderings add to the count a. b. How many ways are there to form postage of 20 cents? Fill in the following chart 10 14 6 8 16 20 0 40 18 Extra Credit:
A small post office has only 4-cent, 6-cent and...
algebraic combinatoric 1. Let b be the number of ways to change 6 cents. Find the generating function ". For whi...
algebraic combinatoric
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued 4 and
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued...
Prove the statement n cents of postage can be formed using just 4-cent and 11-cent stamps...
Prove the statement n cents of postage can be formed
using just 4-cent and 11-cent stamps using mathematical induction,
where n ≥ 30.
Click and drag the given steps (on the right) to the corresponding step names given on the left) to carry out the inductive steps of the proof, after the inductive hypothesis has already been assumed in (b). Step 1 Replace eight 4-cent stamps by three 11-cent stamps, and we have formed k+ 1 cents in postage (3....
1. Using generating functions, find the number of ways to make change for a $100 bill...
1. Using generating functions, find the number of ways to make change for a $100 bill using only dollar coins and $1, $2, and $5 bills. explain in detail
Find a generating function for the number of ways to make n cents in change using...
Find a generating function for the number of ways to make n cents in change using only pennies, nickels, and dimes.
which of the following probabilistic operations would be used to find the number of ways 10...
which of the following probabilistic operations would be used to find the number of ways 10 things could be placed into two groups if order does not matter a factorial b permutation c combination d factorization
3. Let P(n) be the statement that a postage of n cents can be formed using...
3. Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 5-cent stamps. The 5 / Induction and Recursion parts of this exercise outline a strong induction proof that P(n) is true for n 18. a) Show statements P(18), P(19), P(20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true forn > 18. a) Show statements P(18), P(19), P (20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive step? d) Complete...
If the order of objects is not of importance, how many ways can nineteen objects be...
If the order of objects is not of importance, how many ways can nineteen objects be selected three at a time? Why is this result different from the result when order matters?There are blank different ways to select three objects at a time. (Type a whole number.) Explain why this result is different from the result when order matters. Choose the correct answer below. A. When order does not matter, picking the first object before the second object is the...
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2....
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2. A b ox 3. Find a1e for each of the following generating functions:
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways...
need steps
A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number of ways to form postage of n cents if the order of the stamps matters, i.e.. different orderings add to the count a. b. How many ways are there to form postage of 20 cents? Fill in the following chart 10 14 6 8 16 20 0 40 18 Extra Credit:
A small post office has only 4-cent, 6-cent and...
algebraic combinatoric
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued 4 and
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued...
Prove the statement n cents of postage can be formed
using just 4-cent and 11-cent stamps using mathematical induction,
where n ≥ 30.
Click and drag the given steps (on the right) to the corresponding step names given on the left) to carry out the inductive steps of the proof, after the inductive hypothesis has already been assumed in (b). Step 1 Replace eight 4-cent stamps by three 11-cent stamps, and we have formed k+ 1 cents in postage (3....
Find a generating function for the number of ways to make n cents in change using only pennies, nickels, and dimes.
3. Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 5-cent stamps. The 5 / Induction and Recursion parts of this exercise outline a strong induction proof that P(n) is true for n 18. a) Show statements P(18), P(19), P(20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive...
4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true forn > 18. a) Show statements P(18), P(19), P (20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive step? d) Complete...
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways are there to select 20 balls? 2. A b ox 3. Find a1e for each of the following generating functions:
1. Find a1s for each of the following generating functions: contains 8 red, 8 white, 8 blue, and 5 green balls, which are identical cept for color. How many ways...
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