Combinatorics on real situations

Author: SolveSheep

Combinatorical problems based on real life situations on a easy-mid difficulty to start understanding the basis this subject.




Not logged in? Click here to log in.
1.0 Combinatorics
Alphanumeric Password Count

A website requires users to create a password that consists of 2 uppercase English letters followed by 3 digits.
How many different passwords are possible if repetition of letters and digits is allowed? (Assume 26 uppercase letters and 10 digits 0-9).
1.0 Combinatorics
Card Hand Combinations

From a standard deck of 52 playing cards, how many different ways can you select exactly 2 aces?
1.0 Combinatorics
City Tour Itinerary

A tourist wants to visit 3 specific cities out of a list of 7 possible cities. The order in which the tourist visits these cities matters.
How many different travel itineraries are possible?
1.0 Combinatorics
Custom Computer Configurations

A computer manufacturer allows customers to customize their orders. There are 3 CPU options, 2 RAM options, and 4 storage options.
How many different custom computer configurations are possible?
1.0 Combinatorics
Daily Outfit Combinations

John is packing for a trip. He has 4 different shirts, 3 different pairs of pants, and 2 different pairs of shoes. Assuming every shirt goes with every pair of pants and every pair of shoes, how many different outfits can he create?
1.0 Combinatorics
Digital Security Codes

A security system requires a 4-digit code. Each digit can be any integer from 0 to 9.
If digits can be repeated, how many different 4-digit codes are possible?
1.0 Combinatorics
Fast Food Meal Deals

A fast-food restaurant offers a meal deal where customers can choose 1 main course from 3 options, 1 side dish from 4 options, and 1 drink from 2 options.
How many different meal deals can be chosen?
1.0 Combinatorics
Grocery Shopping Combinations

A shopper needs to buy 1 type of fruit from 5 available options, 1 type of vegetable from 4 available options, and 1 type of drink from 6 available options.
How many different combinations of these three items can they choose?
1.0 Combinatorics
Group Photo Lineup

6 friends are lining up side-by-side for a group photo.
In how many different orders can they arrange themselves?
1.0 Combinatorics
Ice Cream Scoop Choices

An ice cream shop has 12 different flavors available.
How many ways can a customer choose 2 different scoops for their cone, if the order of the scoops does not matter?
1.0 Combinatorics
Letter Arrangements

How many distinct 4-letter arrangements can be made using the letters M, A, T, H if each letter can be used only once?
1.0 Combinatorics
License Plate Combinations

A certain state's license plates consist of 3 letters followed by 3 digits.
If repetition of letters and digits is allowed, how many different license plates are possible? Assume there are 26 possible letters and 10 possible digits (0-9).
1.0 Combinatorics
Lottery Ticket Selections

In a local lottery, players choose 4 distinct numbers from the integers 1 to 20. The order in which the numbers are chosen does not matter.
How many different lottery tickets are possible?
1.0 Combinatorics
Meeting Schedule Permutations

There are 4 different meetings that need to be scheduled for Monday afternoon, one after another.
In how many different orders can these meetings be scheduled?
1.0 Combinatorics
Movie Seating Arrangement

7 friends are going to watch a movie and sit in a single row of 7 seats.
In how many different orders can they sit?
1.0 Combinatorics
Multiple Choice Quiz Answers

A quiz consists of 5 multiple-choice questions. Each question has 4 possible answers (A, B, C, D), and only one is correct.
How many different ways can a student answer all 5 questions, regardless of correctness?
1.0 Combinatorics
Music Playlist Creation

A music streaming service allows users to create playlists. If a user has 10 favorite songs and wants to create a playlist of 4 songs, where the order of the songs matters, how many different playlists are possible?
1.0 Combinatorics
Pizza Topping Choices

A pizza restaurant offers 8 different toppings. A customer wants to choose exactly 3 different toppings for their pizza.
How many different combinations of toppings are possible?
1.0 Combinatorics
Restaurant Menu Selections

A restaurant offers a fixed-price menu where customers choose one appetizer, one main course, and one dessert. There are 5 choices for appetizers, 8 choices for main courses, and 4 choices for desserts. How many different three-course meal combinations are possible?
1.0 Combinatorics
Selecting a Basketball Team

A basketball coach needs to select a starting lineup of 5 players from a squad of 12 players.
How many different starting lineups are possible, assuming the order of players in the lineup does not matter?
1.5 Combinatorics
Arranging Books on a Shelf

Jessica has 7 distinct books she wants to arrange on a bookshelf.

a) In how many different ways can she arrange all 7 books?

b) If 3 of the books are history books and must be kept together, in how many ways can she arrange the books?
1.5 Combinatorics
Marble Selection from a Bag

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
If you pick 3 marbles at random, how many ways can you pick exactly 1 red, 1 blue, and 1 green marble?
1.5 Combinatorics
School Committee Formation

A school club has 15 members, consisting of 8 boys and 7 girls. They need to form a committee of 4 members.

a) How many different committees can be formed?

b) How many different committees can be formed if it must consist of 2 boys and 2 girls?
1.5 Combinatorics
Striped Flag Design

A flag has 3 horizontal stripes. There are 5 different colors available to choose from.
How many different flags can be designed if adjacent stripes must have different colors?
2.0 Combinatorics
PIN Code Possibilities

A bank requires its customers to create a 4-digit Personal Identification Number (PIN) using digits from 0 to 9.

a) How many different 4-digit PINs are possible if digits can be repeated?

b) How many different 4-digit PINs are possible if digits cannot be repeated?

c) How many different 4-digit PINs are possible if the first digit cannot be 0 and digits cannot be repeated?