Discrete Mathematics with Graph Theory (3rd Edition) 214

Discrete Mathematics with Graph Theory (3rd Edition) 214 -...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
212 Solutions to Review Exercises 2. As a group, the girls can be arranged in 6! ways. Then, together with the boys, they form 8 "units" to be arranged in a row. Since the girls cannot appear first, there are seven choices for the first position in the row. Then there are six choices for the last position (again, not the girls). There are 6! ways to fill out the remaining positions, so the answer is 7(6)(6!)(6!) = 21,772,800. 3. The answer is zero! In a circle, if the six girls are together, then the boys must also be together. 4. Let A be the set of permutations containing aeb and B the set of permutations containing bef. We want IA UBI. By the Inclusion-Exclusion Principle, this is IAI + IBI-IA n BI. Now IAI = 4! (aeb is a single unit in a string of four "units"), IBI = 4! and IA n BI = 2! (if both aeb and bef appear, then aebef must appear). Thus IA U BI = IAI + IBI- IA n BI = 24 + 24 - 2 = 46. 5. (a) Let W, P and J denote, respectively, those permutations in which "wendy", "patrick" and "josh" appear. Then IWI = 22! (arrange the 22 blocks consisting of "wendy" and the 21 letters of
Image of page 1
This is the end of the preview. Sign up to access the rest of the 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