Multiplication Counting Principle
Read this topicExplanations 4
- The multiplication counting principle states that the number of ways a sequence of events can occur is the product of the number of ways each individual event can occur. Example…
By Vinitha Ranganeni, Dario Teran, Elise Molinaro, Alex Federspiel, Ruiran Xun, Joshua Siktar
- (Video) The Counting Principle, Permutations, and Combinations by Jack Walker Jack Walker has a great video on the multiplication counting principle, permutations, and combinati…
By Ben Ferrara, Alex Federspiel, Joshua Siktar, Amy Feraco
- What is the multiplication counting principle? Imagine that you're making cupcakes. You've got four types of icing and three types of sprinkles. How many possible (delicious) cu…
By Hannah Bonville, Alex Federspiel, Joshua Siktar
- Counting Sizes of Cartesian Products One particular instance of the Multiplication Counting Principle is in finding the sizes of Cartesian products of sets. If AAA and BBB are s…
By Joshua Siktar
Problems 27
- Every day your lunch consists of a sandwich, a fruit, a drink, and a cookie. If you have 333 types of sandwiches, 444 types of fruit, 555 types of drinks and 333 types of cookie…
- True or False\text{True or False}True or False === If you have nnn types of pants and mmm types of shirts, you have n+mn+mn+m different possible outfits.
- You are planning your vacation. Over the 444 days you have a variety of things to choose from. The first day you have four different hiking trails you could take. The second day…
- A test you are taking has twenty-four multiple choice questions, each with answers AAA, BBB, CCC, and DDD. How many possible solution sets are there for this test?
- How many 333 letter words can you make if you don't care if it is a real word or not, and you are allowed to repeat letters?
- Among the first 100010001000 positive integers, there are nnn whose hexadecimal representation contains only numeric digits. What is nnn? (AMC)
- Find the number of possible different functions f :{0,1}→{0,1}f\colon \{0,1\}\to \{0,1\}f:{0,1}→{0,1}.
- Which of the following could be true?
- Say there are xxx ways of doing something and yyy ways of doing another. Which of these represents the number of ways of doing both xxx and yyy?
- You are buying a new bike and have the following options to chose from. Based off the options above, how many different choices of bike do you have?
- The expizzaria has the following combinations of pizza. Using the information above, determine how many different choices of pizza you could order in all?
- CeCee is looking to buy a new violin. She is 777 years old and doesn't have a preference of what kind of violin she gets. Using the guide above, how many different options does …
- You are shopping at the gift shop to find a candle for your friend. You see in the candle aisle that there are 333 sizes, 444 colors, and 333 types of candles available. Which o…
- Consider the two sets: {B, J, K} & {X, Y} Which of the following sets represents all of the ordered pairs for these components?
- Your friend Amanda owns her own custom card business. You go to her to custom make a graduation card for your friend. The options are the following: 333 sizes 777 colors 444 phr…
- Jess is looking to purchase a new lamp for her apartment. She goes to the store and is faced with the following options. Considering these options, how many different lamps does…
- Fill in the blanks from top to bottom for the tree diagram above.
- Consider the fast food menu above. A meal combo consists of a sandwich, a side, and a drink. How many different meal combinations are available given the menu above?
- Michael works for a governmental agency, making passwords for top-secret databases. Each character of the password can be any one of 2∗1032*10^32∗103 symbols. If the password is…
- Bert the Baker is an expert cupcake maker. His cupcake business has more color options than any other cupcake business in the world! If there are 4∗1054*10^{5}4∗105 color shades…
- You have exactly 100\100100. You can purchase tickets on your own or work with friends to pool your money. Which of these is the best strategy?
- ESPN's website says that it only takes 555 minutes to fill out a bracket form. About how long would it take to fill out enough bracket forms to guarantee a win of Buffett's priz…
- You want the codes to be as short as possible. How short can your codes be while still being able to uniquely cover 100,000100,000100,000 different words?
- In the snail park, there are two sets of four parallel paths, where the lines that are not parallel intersect each other at right angles. You want to place a snail at one endpoi…
- You have 414141 articles of clothing in your closet: 888 shirts, 888 pants/skirts, 555 pairs of shoes, 444 belts, 444 jackets, 444 pairs of gloves, 444 hats, and 444 ties/scarve…
- I flip the same coin 555 times and record the sequence. Every time I flip a head, I write down an HHH and every time I flip a tail I write down a TTT. How many different sequenc…
- Daniel is making a sandwich and can choose for 222 types of bread and 888 types of meat. Syliva is also making a sandwich and has 444 types of bread and xxx types of meat. Given…