A quarter, a nickel, and a dime are all flipped. How many possible outcomes are there?

Two six-sided dice are thrown at the same time from a cup. They are all identical. How many distinct outcomes are there?

Two identical six-sided dice are thrown. How many distinct outcomes sum to 7?

How many permutations are there of the names Moe, Larry, and Curly?

You have five people, and four distinct jobs that need to be done. How many ways can you assign four out of the five people to jobs?

In a group of 3 men and 2 women, you are to select a committee of two people. How many ways can you do that?

In a shipment of 10 widgets, 2 are defective. How many ways can you choose a sample of 3 widgets in which at least one is defective?

Suppose there are large piles of red and blue marbles. How many ways can you choose four marbles?

One fair eight-sided die is rolled. What is the probability of getting a result less than 5?

10. A family has three children. It is equally likely for a boy or a girl to be born. What is the probability that exactly two of the children will be girls?

True or false. The pigeonhole principle dictates that if 8 events are scheduled to happen during the course of a week, at least two events must happen on the same day

If a family has three children, and it is equally likely each child is a girl or boy, what is the likelihood that two children will be boys, given that one is a girl?

Two dice are rolled. What is the probability of getting a sum of 12?

How many eight-bit binary (all digits are 1's or 0's) strings exactly contain four 1's?

How many eight-bit binary strings contain two or fewer ones?

In a complete graph (edge between every pair of vertices) with ten vertices, how many edges would make up a spanning tree?

How many edges are there in a complete, undirected bipartite graph with 3 vertices in one half of the partition and 3 in the other??

How many edges are there in the complete, undirected graph with 7 vertices?

How many vertices are there in an n-dimensional cube graph?

In the graph {(a,b),(b,c),(c,d),(d,a) is there an Euler cycle?

In the graph of question 20, is there a Hamiltonian cycle?

In a graph where every vertex has degree 4, is there an Euler cycle?

Can a graph with 10 vertices and 7 edges be connected?

Is it true that in a graph where every vertex has degree 2, there must be a Hamiltonian cycle?

How many edges would be in a spanning tree in a graph with n vertices?

True or false: the elements along the diagonal of an adjacency matrix representation of a graph correspond to self-edges, i.e. edges of the form (a,a) where a Is a node in the graph.

If every node in a binary tree has two children except the leaf (terminal) nodes, and the longest path in the graph from the root to a leaf has 3 edges, can there be 7 nodes in the graph?

A binary tree with n nodes were every leaf node is exactly the same distance from the root, has how many nodes?

True or false, A graph without a spanning tree is not a connected graph

True or false, depth-first search involves backtracking

Let A = {1,2,3,4}, B= {2,3,4,5,6}, C= {6} . What is(A Intersect B) union C?

The set {x | x^2- 2 = 0 and x is a real number} is empty.

True or false: The intersection of the set of real numbers greater than 1 and the set described in problem 32 is empty.

p v (q ^ r) where p = T, q = F, r= T

The statements if it is raining outside, it is cloudy and either it is cloudy or it is not raining outside are logically equivalent

To determine the truth or falsehood of the statement There are other fish in the sea, where would you look?

The statement There is a non-blue fish and Not all fish are blue are logically equivalent

The deduction All engineers study math or science. John studies math. Therefore John is an engineer is valid

The negation of the proposition There is a blue fish starting with All fish is what?

Over the set of real numbers, the complement of the set of numbers whose square is 4 is what?

Finding a counterexample proves that a statement is true or false?

True or False: To prove a proposition of the forma -> b is true, it is enough to show that the proposition if b is false, then a is false .

True or false: The following set defines a relation between sets {a,b,c,d} and range {1,2,3} : {(a,1),(b,1),(c,1)} . In order to make this relation a function, how would you restrict set {a,b,c,d} to be the domain of the function

In question 43, is the function 1-1

In question 44, is the function onto

True or false: an infinite increasing sequence of integers can have an upper bound.

True or false: an infinite increasing sequence of real numbers can have an upper bound.

Is the relation {(x,y) | x and y are real numbers and x = y} symmetric?

How can one tell if a relation is symmetric if it is represented by a matrix A

A database consisting of 30 columns and two rows can be considered a relation on the records in the database