Learning Materials
Features
Discover
Chapter 1: Q. 1.15 (page 16)
A dance class consists of students, of which are women and 12 are men. If men and women are to be
chosen and then paired off, how many results are possible?
The possible results are.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
If people are to be divided into committees of respective sizes and how many divisions are possible?
How many different letter arrangements can be made from the letters (a) Fluke? (b) Propose? (c) Mississippi? (d) Arrange?
Consider a tournament of contestants in which the outcome is an ordering of these contestants, with ties allowed. That is, the outcome partitions the players into groups, with the first group consisting of the players who tied for first place, the next group being those who tied for the next-best position, and so on. Let localid="1648231792067" denote the number of different possible outcomes. For instance, localid="1648231796484" , since, in a tournament with localid="1648231802600" contestants, player localid="1648231807229" could be uniquely first, player localid="1648231812796" could be uniquely first, or they could tie for first.
(a) List all the possible outcomes when .
(b) With localid="1648231819245" defined to equal localid="1648231826690" , argue without any computations, that localid="1648281124813"
Hint: How many outcomes are there in which localid="1648231837145" players tie for last place?
(c) Show that the formula of part (b) is equivalent to the following:
localid="1648285265701"
(d) Use the recursion to find N(3) and N(4).
Consider three classes, each consisting of students. From this group of students, a group of students is to be chosen.
(a) How many choices are possible?
(b) How many choices are there in which all students are in the same class?
(c) How many choices are there in which of the students are in the same class and the other student is in a different class?
(d) How many choices are there in which all students are in different classes?
(e) Using the results of parts (a) through (d), write a combinatorial identity.
If Americans, French people, and British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine