What Is the Fundamental Counting Principle?
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- Fundamental Counting Principle You and your friend are in the same class and you have a quiz coming up. Going in, you know that the quiz is going to be 101010 multiple choice qu…
By Jonathan Heller
- The Fundamental Counting Principle The Fundamental Counting Principle seems very straightforward, but it is one of the foundational theories in probability. It is a quick way to…
By Anusha Rahman
- (Video) Fundamental Counting Principle by Mario's Math Tutoring In this video by Mario's Math Tutoring, you will learn about the Fundamental Counting Principle and how to use it.
By Anusha Rahman
Problems 16
- Let p,qp,qp,q be positive integers such t hat q≥pq\ge pq≥p. How many one-to-one functions are possible from a set AAA containing ppp elements to a set BBB containing qqq elements?
- How many positive even numbers have an even number of digits and are less than 100001000010000? Source: 2011-2012 Winter Online Math Open
- There are 29 unit squares in the diagram above. A frog starts in one of the five (unit) squares on the top row. Each second, it hops either to the square directly below its curr…
- Dirock has a very neat rectangular backyard that can be represented as a 32×3232\times 3232×32 grid of unit squares. The rows and columns are each numbered 1,2,…,321,2,\ldots, 3…
- Master Chef Dan Hu can make four specialties: cereal, canned soup, scrambled eggs, and cookies. He can choose to make one specialty every day from Monday to Friday (inclusive), …
- How many ways are there to order the letters of "MATHEMATIC" (without an S at the end)?
- Imagine yourself in elementary school. Whenever you were to walk down the hall, you and your classmates are to stand in a line. You have a whimsical teacher that loves to "shake…
- How many different license plates are there with two letters followed by three digits, assuming that the letters cannot be I or O, and the digits cannot be 1 or 0?
- You are in a dessert shop, and you must build your dessert. You need to pick a flavor of ice cream, a fruit, and a topping. The ice cream flavors are vanilla, chocolate, and str…
- There are NNN students in a class. Each possible nonempty group of students selected a positive integer. All of these integers are distinct and add up to 201420142014. Compute t…
- A lock’s combination consisting of three different numbers in the range 0-59 (inclusive) that must be dialed in order. How many different combinations are possible?
- How many subsets are there of a set of size 8?8?8?
- How many four digit integers with alternate odd and even digits but with no repeat digits are there?
- How many different integers can be formed by multiplying some or all of the digits {2,3,4,4,5,5,5}?\{2, 3, 4, 4, 5, 5, 5\}?{2,3,4,4,5,5,5}?
- How many four-digit numbers without repeated digits are there? eg. 2378 and 1894 is ok, but 2372 and 1557 is not.
- Each table seats 121212 people, with seat positions numbered 111 through 12.12.12. Kanye and Taylor cannot sit next to or across from each other. How many ways are there to arra…