Counting and probability

Decide whether order matters, then count the complement when 'at least one' appears. A probability is favorable outcomes over equally likely outcomes.

A lesson for this area

Problem 1AMC 8

A cafe offers $4$ soups, $3$ sandwiches, and $5$ drinks. A lunch special consists of one soup, one sandwich, and one drink. How many different lunch specials are possible?

Problem 2AMC 8

A bag contains $3$ red marbles, $5$ blue marbles, and $4$ green marbles. One marble is drawn at random, with each marble equally likely to be drawn. What is the probability that the marble drawn is not blue?

Problem 3AMC 8

How many three-digit positive integers have three different digits, all of which are odd?

Problem 4AMC 8

Two fair six-sided dice, each with faces numbered $1$ through $6$ , are rolled. What is the probability that the two numbers rolled differ by exactly $2$ ?

Problem 5AMC 8

Each of $5$ friends sends exactly one text message to each of the other $4$ friends. How many text messages are sent in all?