Q1. A vending machine dispensing books of stamps accepts only one-dollar coins, $1 bills, and $5 bills. a) Find a recurrence relation for an, the number of ways to deposit n dollars in the vending machine, where the order in which the coins and bills are deposited matters. ( Hint: 3 cases: Case1; the first deposit is a one-dollar coin, Case 2: First deposit is a $ 1 bill. Case 3: First deposit is a $ 5 bill Note that your recurrence relation is valid for n 2 6 So we will need 5 initial conditions a1,a2,a3,a4,a5. b) In how many ways can you deposit $8 for a book of stamps? Use the recurrence relation that you found in part (a).
Q1. A vending machine dispensing books of stamps accepts only one-dollar coins, $1 bills, and $5 bills. a) Find a recurrence relation for an, the number of ways to deposit n dollars in the vending machine, where the order in which the coins and bills are deposited matters. ( Hint: 3 cases: Case1; the first deposit is a one-dollar coin, Case 2: First deposit is a $ 1 bill. Case 3: First deposit is a $ 5 bill Note that your recurrence relation is valid for n 2 6 So we will need 5 initial conditions a1,a2,a3,a4,a5. b) In how many ways can you deposit $8 for a book of stamps? Use the recurrence relation that you found in part (a).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 57EQ
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