Question

Using generating functions, find the number of ways to make change for a 100 dollar bill using only dollar coins and $1, $2, and $5 bills.

Answer #1

Discrete Math question (generating functions)
Use the generating function method to find how many ways 10
identical Green Tree Pythons can be distributed within four
numbered cages, where the first two of their new homes require an
even (but non-zero) number of snakes, the third cage must have an
odd number, and with the last cage holding at least three
reptiles?

Homework Question 9: (10 pts) Show your work
a) Use generating functions to determine the number of different
ways ten cookies can be distributed among three children so that
each child receives at least two cookies but no more than five. (4
pts)
b) Find the closed form for the generating functions for the
following sequence: 0,0,1,2,4,8,… (3 pts)
c) Find the coefficient of x^8 in the power series expansion of
G(x)=x^2/(1+5x) (3 pts)

Use exponential generating functions to find the number of
r-digit ternary sequences with at least one 0 and at least one
2.

This is a Combinatorics question.
Find a generating function for ar, the number of
ways:
(A)
To distribute r identical objects into seven distinct
boxes with an odd number of objects not exceeding nine in the first
three boxes and between four and ten in the other boxes.

Find the generating function to determine the number of ways to
pick k objects from 2n objects numbered from 1 to 2n when each
odd-numbered object appears an even number of times.

count the number of ways to make change for n cents with
pennies, nickels, dimes, and quarters

Use exponential generating functions to determine the number of
strings of length 12 with the following properties:
1) Each string is made up of the characters ”a”, ”b”, ”c”, ”d”
(some characters may not appear at all).
2) The number of times that ”a” appears is even, and the number
oftimes that ”b” appears is odd.
Find a closed-form formula for the exact answer – e.g. I’m
looking foran answer like 5n+ 2n, not∑ni=12n(3ni).

Construct a C program which computes the minimum number of bills
and coins needed to make change for a particular purchase. The cost
of the item is $21.17 and the amount tendered is $100.00. These
values should be built into your program using assignment
statements rather than input into the program during program
runtime. Your program should indicate how many bills and coins of
each denomintaion are needed for the change. You should make use of
the following denominations: Bills:...

1. For the following functions, find ∆y (the exact change) and
dy (the approximate change from a linear approximation) for the
given functions.
(i) f(x) = x + 4/x , x = 2, ∆x = .1
(ii) f(x) = x/ln (x2 + 3), x = 3, ∆x = .5
2. A pretzel vendor at a dodgers game sells 920 pretzels per
game at a price of $4.00. For every $0.50 decrease in price an
additional 20 pretzels are sold. The...

10. Show that (1-x-x^2-x^3-x^4-x^5-x^6)^-1 is the generating
function for the number of ways a sum of r can occur if a die is
rolled any number of times

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