{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern