![]() ![]() When the spinner gets spun, there are eight possible outcomes: They usually involve equally-spaced intervals that are numbered, like this diagram will demonstrate.Ī played spins an arrow that is attached to the dial and a space is indicated by the pointer. Spinners are used in games to randomize moves on a board. There are 6 outcomes for the first roll and 8 outcomes for the second roll. We will use the fundamental counting principle. If someone asked this following question, however there is a different level of response.įor certain game, one has to roll a 6-sided die and an 8-sided die. One can see there are six possible outcomes. If a 6-sided die is rolled, these are the possible outcomes: Let it be known that there are dice that have 10-sides, 20-sides, and other numbers of sides. The above image shows two traditional 6-sided dice. Again, the fundamental counting principle is what must be used.įirst, we should take a look at various randomizers. In order to calculate probabilities, one must first calculate the number of total possible outcomes. There are games that use dice, spinners, and other randomizers. This login system will give us 3,872,103,691,346,280 unique logins! That is more than 3.8 quadrillion possible logins, which is more logins than any website will ever need. Here is how this login system works – broken down by position. How many different logins can this system allow? However, the middle seven characters can be letters, numbers and special characters. The first character has to be a letter and the last character has to be a number. This login system will give us 29,536,122,503,680 unique logins! That is more than 29 trillion possible passwords, which is a sufficient number of passwords to keep data safe.Ī certain website allows for nine characters for its login. Here is how this password system works – broken down by position. How many different passwords can this system allow? However, the middle six characters can be letters and numbers. ![]() Some websites allow password data to contain special characters, like these symbols: #, %, !, $, +, -, and $.Ī certain website allows for eight characters for its password. Keep in mind, that login and password data can usually contain both uppercase and lowercase letters and numbers. This section will explain how to count the number of logins and the number of passwords a website may use. No two users can have the same login so, it is important for website developers to create login systems that have a lot of possibilities to allow for a large number of users. Many websites that keep track of data for users require a login and password. Ideo: The Fundamental Counting Principle: License Plate Problems So, this license plate system is good for producing over 20 million different plates for over 20 million different vehicles. This means the first two characters have 24 outcomes each and the last three characters have 24 + 9, or 33 characters each. Here is a table that outlines our situation.įor letters A – Z without the Os and Qs, there are 24 characters.įor numbers 1 – 9, there are 9 characters. How many unique license plates can be made? The last four characters can be either letters (no Os or Qs) or numbers 1 – 9. The first two characters must be letters, but the letters O and Q cannot be used. So, this license plate system is good for producing over 1.1 billion different plates for over 1.1 billion different plates.Ī certain state uses license plates that have five characters. Using the fundamental counting principle, we get this set-up. This means the first two characters have 26 outcomes each and the last four characters have 26 + 10, or 36 characters each. Each blank below represents a possible character on a plate.įor letters A – Z, there are 26 characters.įor numbers 0 – 9, there are 10 characters. ![]() To figure out this problem, we need to look at all the options for each character. The last four characters can be either letters or numbers. The first two characters must be letters. ![]() Keep in mind, small case letters are never used on license plates.Ī certain state uses license plates that have six characters. Here is a situation that an official has to count to determine the number of different plates that can be produced. So, officials have to be able to count the number of plates it produces. Each vehicle has to have its own unique plate. When state government officials issue license plates, they have to make sure there are enough plates for the people who drive in their state. ![]()
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