How many ways can n books be placed on k distinguishable shelves?
a) if the books are indistinguishable copies of the same title?
b) if no two books are the same, and the positions of the books on the shelves matter?

How many ways are there to deal bands of five cards to each of six players from a deck containing 48 different cards?

How many ways are there to select three unordered elements from a set with five elements when repetition is allowed?

There are 2504 computer science students at a school. Of these, 1876 have taken a course in Java, 999 have taken a course in Linux, and 345 have taken a course in C. Further, 876 have taken courses in both Java and Linux, 231 have taken courses in both Linux and C, and 290 have taken courses in both Java and C. If 189 of these students have taken courses in Linux, Java and C, how many of these 2504 students have not taken a course in any of these three programming languages?

a. If the books are indistinguishable copies of the same title?
Solution:
There are k distinguishable shelves and n books are to be placed in them.
If the shelves are represented by space between two sticks | | and books are represented by *, then
| | * * * | | * * | | | ..... | (Total of k + 1 sticks for k shelves and n *s for n books)
Assume that the first and last sticks are fixed. Hence there are (k+1-2) + n items between the first and last sticks. Out of these n books have to be placed. Hence the number of ways = (k + 1 - 2 + n) C (n)
= (n + k - 1) C (n)

b. If no two books are the same, and the positions on the shelves matter?
Solution:
There are k distinguishable shelves and n distinguishable books.
For each book, there are k possible ...

Solution Summary

Clear explanation and explanation has been provided for the attached questions.

1. List the ordered pairs in the equivalence relations produced by these partitions of {0,1,2,3,4,5}
a) {0}, {1,2}, {3,4,5}
b) {0,1}, {2,3}, {4,5}
c) {0,1,2}, {3,4,5}
d) {0}, {1}, {2}, {3}, {4}, {5}
2. Which of these collections of subsets are partitions of the set of integers?
a) the set of even integers and the set of

A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.
a) Use the counting principle to determine the number of points in the sample space.
b) Describe how a tree diagram would represent this si

A.) Show that the following set is infinite by setting up a one-to-one correspondence between the given setand a proper subset of itself: {8,10,12,14,...}
b.) Show that the following set has cardinal N sub o by setting up a one-to-one correspondence between the set of counting numbers and the given set:
{5,9,13,17,...}

Definition: For any E in X, where X is any set, define M(E) = infinity if E is an infinite set, and let M(E) be then number of points in E if E is finite. M is called the counting measure on X.
Let f(x) : R -> [0,infinity)
f(j) = { a_j , if j in Z, a if j in RZ}
( Z here is counting numbers, R is set of real numbers)

Create three sets, set A, set B, andset C by going through the items in your wallet or purse.
Set A will be a list of all of these items.
Create Set B, from the items in Set A that you think are essential.
Create Set C, by taking the complement of Set B in Set A, i.e. all of the non-essential items in your wallet or

A sale representative must visit 4 cities: Omaha, Dallas, Wichita, and Oklahoma City. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.