{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Doc4Afterm

# Doc4Afterm - 2 Determine the generating function for the...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2. Determine the generating function for the number of ways to distribute 35 pennies {from an unlimited supply} among ﬁve children if {a} there are no restrictions; (h) each child gets at least 11:; {c} each child gets at least 21:; {d} the oldest child gets at least lite; and (e) the two youngest children must each get at least 101:. 4. 3) Explain why the generating function for the number of ways to have :1 cents in pennies and nickels is {1+x+x2+x3+---}(l+x5+x'"+---}. 2. Detenuine the sequence generated by each of the following generating functions. a) f(I}= {Ex—3F b} for} =x‘ftl —x) c} for) =x3ﬂil erg} d) for} = 1m +3x} e) fix} = lft3-x) r) fix1=l;(1—x)+3x"-11 II. Determine the constant (that is, the coefﬁcient of x”} in {3x2 - (2a))”. 15. In how many ways can Traci select :2 marbles from a large supply of blue. red, and yellow marbles {all of the same size] if the selection must include an even number of blue ones? 6. What is the generating function for the number of partitions of n E N into summands that {a} cannot occur more than ﬁve times; and {b} cannot exceed 12 and cannot occur more than ﬁve times? 8. Show that the number of partitions of n IE 2+ where no summand is divisible by 4 equals the number of partitions of n where no even summarid is repeated {although odd stunmands may' or mayr not be repeated). ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern