Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a) How many re-arrangements are there of the words PHILIPP, PHILIP, and PHILLIP? Which one has the most, which one the fewest re-arrangements? Show all your working and justify your answers.

(a) How many re-arrangements are there of the words PHILIPP, PHILIP, and PHILLIP? Which one has the most, which one the fewest re-arrangements? Show all your working and justify your answers.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 5CT: A commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The...
See similar textbooks
icon
Related questions
Question
Ex 2 discrete math
(a) How many re-arrangements are there of the words PHILIPP, PHILIP, and PHILLIP? Which one has the most, which one the fewest re-arrangements? Show all your working and justify your answers. (b) Consider the (nx n)-grid (drawn below in the case n = 6). How many distinct walks are there from the bottom left corner to the top right corner, if you are only allowed to go up or to the right? How many distinct walks are there in a 3-dimensional (nx nx n)- grid from the bottom left front corner to the top right back corner, if you are only allowed to go up, right, or to the back? Show all your working and justify you answers. (c) How many surjective functions f: {1, 2, 3, 4, 5} → {1, 2} are there if f(1) = 1? How does this number change if f(1) = 1 and f(2)= 2? Show all your working and justify your answers.
Transcribed Image Text:(a) How many re-arrangements are there of the words PHILIPP, PHILIP, and PHILLIP? Which one has the most, which one the fewest re-arrangements? Show all your working and justify your answers. (b) Consider the (nx n)-grid (drawn below in the case n = 6). How many distinct walks are there from the bottom left corner to the top right corner, if you are only allowed to go up or to the right? How many distinct walks are there in a 3-dimensional (nx nx n)- grid from the bottom left front corner to the top right back corner, if you are only allowed to go up, right, or to the back? Show all your working and justify you answers. (c) How many surjective functions f: {1, 2, 3, 4, 5} → {1, 2} are there if f(1) = 1? How does this number change if f(1) = 1 and f(2)= 2? Show all your working and justify your answers.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS