3 salads, 4 main dishes, and 2 desserts Total meal combinations are found by multiplying each salad, main dish, and dessert using the fundamental rule of counting. The fundamental rule of counting states, if there are a ways of doing one thing, b ways of doing another thing, and c ways of doing another thing, than the total combinations of all the ways are found by a * b * c. With 3 salads, 4 main dishes, and 2 desserts, our total meal combinations are: 3 * 4 * 2 = [B]24 different meal combinations.[/B]

5 shirts. 3 pants and 8 shoes how many outfits can you wear Using the fundamental rule of counting, we can have: 5 shirts * 3 pants * 8 shoes = [B]120 different outfits[/B]

7 salads, 10 main dish, 6 dessert Using the Fundamental Rule of Counting, we have: 7 * 10 * 6 = 420 possible meals

A numerical pass code is required to open a car door. The pass code is five digits long and uses the digits 0-9. Numbers may be repeated in the pass code. How many different pass codes exist? 0-9 is 10 digits. Since digits can repeat, we use the fundamental rule of counting to get: 10 * 10 * 10 * 10 * 10 = [B]100,000 different pass codes[/B]

A restaurant offers 20 appetizers and 40 main courses, how many ways can a person order a two course meal? Using the fundamental rule of counting, we can have: 20 appetizers * 40 main courses = [B]800 possible two-course meals[/B]

A restaurant offers the following options: [LIST] [*]Starter – soup or salad [*]Main – chicken, fish or vegetarian [*]Dessert – ice cream or cake [/LIST] How many possible different combinations of starter, main and dessert are there? Using the fundamental rule of counting, we have: 2 starters * 3 main courses * 2 desserts = [B]12 different combinations [MEDIA=youtube]-N9j7FQ8Le4[/MEDIA][/B]

A three digit number, if the digits are unique [LIST=1] [*]For our first digit, we can start with anything but 0. So we have 9 options [*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options [*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options [/LIST] Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting: 9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

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Alice is making a sandwich to pack in her lunch. She has 2 different kinds of bread, 3 cheeses, 4 lunch meats, and 2 condiments to choose from. Assuming she uses one of each of bread, cheese, meat, and condiment, how many different sandwiches can she make? We use the Fundamental Rule of Counting [LIST] [*]Bread: 2 [*]Cheeses: 3 [*]Lunch Meats: 4 [*]Condiments: 2 [/LIST] 2 * 3 * 4 * 2 = [B]48 different sandwiches[/B]

An ice cream shop carries 6 ice cream flavors, 3 sauces, and 4 toppings. If a sundae has one scoop of ice cream, one sauce, and one topping, how many different sundaes can be created? Using the rule of counting, we have: We have 6 possible ice cream flavors * 3 possible sauces * 4 possible toppings = [B]72 possible sundaes[/B]

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camille has 7 blouses,2 skirts,3 pair of short pants and 5 pair of jeans.how many different outfits can he wear,assuming that he always wear a belt. Using the fundamental rule of counting, we find total amount of different outfits as follows: 7 blouses * 2 skirts * 3 pair of short pants * 5 pair of jeans = [B]210 outfits[/B].

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Consider the first 8 calculations of 7 to an exponent: [LIST] [*]7^1 = 7 [*]7^2 = 49 [*]7^3 = 343 [*]7^4 = 2,401 [*]7^5 = 16,807 [*]7^6 = 117,649 [*]7^7 = 823,543 [*]7^8 = 5,764,801 [/LIST] Take a look at the last digit of the first 8 calculations: 7, 9, 3, 1, 7, 9, 3, 1 The 7, 9, 3, 1 repeats through infinity. So every factor of 4, the cycle of 7, 9, 3, 1 restarts. Counting backwards from 2013, we know that 2012 is the largest number divisible by 4: 7^2013 = 7^2012 * 7^1 The cycle starts over after 2012. Which means the last digit of 7^2013 = [B]7 [MEDIA=youtube]Z157jj8R7Yc[/MEDIA][/B]

Free Fundamental Rule of Counting Calculator - Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

if joey has 5 swimsuits, 3 bicycles, and 4 pairs of running shoes, how many ways are there for joey to choose Using the Fundamental Rule of Counting, we have: 5 swimsuits * 3 bicycles * 4 pairs of running shoes = [B]60 possible choices[/B]

if you own 5 pants, 8 shirts, and 3 jackets how many outfits can you make wearing 1 of each item? Using the Fundamental Rule of counting, we have: Total Pants * Total Shirts * Total Jackets 5 * 8 * 3 [B]120 [/B]

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License plate that is made up of 4 letters followed by 2 numbers Using the fundamental rule of counting, we have: 26 possible letters * 26 possible letters * 26 possible letters * 26 possible letters * 10 possible numbers * 10 possible numbers = [B]45,697,600 license plate combinations[/B]

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed We have 26 letters A-Z and 10 possible digits 0-9. Using the fundamental rule of counting, we have: 26 * 26 * 26 * 10 * 10 = [B]1,757,600 possible choices[/B]

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetition of letters and digits is allowed We have 26 letters in the alphabet We have 10 digits [0-9] The problem asks for the following license plate scenario of Letters (L) and Digits (D) LLLDDD The number of plates we can make using L = 26 and D = 10 using the fundamental rule of counting is: Number of License Plates = 26 * 26 * 26 * 10 * 10 * 10 Number of License Plates = [B]17,576,000[/B]

Lisa has 5 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other? Using the fundamental rule of counting, we have: 5 * 10 * 4 = [B]200 different 3-piece outfits[/B]

the sum of 3 consecutive natural numbers, the first of which is n Natural numbers are counting numbers, so we the following expression: n + (n + 1) + (n + 2) Combine n terms and constants: (n + n + n) + (1 + 2) [B]3n + 3 Also expressed as 3(n + 1)[/B]