Combinatorics - practice problems - page 8 of 50
Combinatorics is a part of mathematics that investigates the questions of existence, creation and enumeration (determining the number) of configurations.It deals with two basic tasks:
How many ways can we select certain objects
How many ways can we arrange certain objects
Number of problems found: 993
- Tournament 7975
Eight players took part in the table tennis tournament. The tournament system allows players to play with each other only once. How many matches will take place in this tournament? - Organized 7966
A group of foreign tourists planned to visit 4 Slovak cities - Košice, Prešov, Poprad, and Kežmarok. They decided that Prešov would be the third city they would visit. How many different ways could they have organized a visit to the listed places? - A pizza
A pizza place offers 14 different toppings. How many different three-topping pizzas can you order? - Created 7758
How many words can be created from the word KLADIVO if we want the word VODA to be written next to each other? - Three-part novel
In how many ways can seven books be stored on a shelf if there is one three-part novel to be placed side by side? - Decorations 7693
Petra was preparing a pudding cup to celebrate the holiday. It had four types of pudding, five types of fruit, and two types of decorations. How many different glasses could she prepare with one pudding, one fruit, and one garnish? - Election 4
In a certain election, there are three presidential candidates: 5 for secretory and 2 for treasurer. Find how many ways the election may (turn out/be held). - A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first five q - Probability 7432
In the department store, they have 100 televisions, of which 85 are of first quality, and 15 are of second quality. The first ten buyers received a premium TV. What is the probability that the eleventh is sold a second-rate TV? - Admittedly 7431
How many ways can three children divide five small and six large exercise books? Admittedly, some get nothing. - Mumbai
A job placement agency in Mumbai had to send ten students to five companies, two to each. Two of the companies are in Mumbai, and others are outside. Two students prefer to work in Mumbai, while three prefer to work outside. How many ways can assignments - A book
A book contains 524 pages. If it is known that a person will select any page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253. - Certificate 6740
There are 19 children in class 6A, 7 subjects, and no one has a worse grade than a three. Can each of them have a different certificate? How many would have to be in the class so that everyone could not have another report card? - Ribbons 6640
Danka knits a sweater and has a choice of seven colors. a) How many ways can he choose three colors for the sleeves? b) He wants ribbons of four colors on his back. How many options does he have to choose from? - Probability 6549
There are 8 balls in the box, and 3 of them are new. For the first game, 2 balls are randomly selected from the box and returned after the game! For the second game, 2 balls are again chosen at random. What is the probability that both have already been u - Dd 2-digit numbers
Find all odd 2-digit natural numbers compiled from digits 1; 3; 4; 6; and 8 if the digits are not repeated. - Assemble 6449
How many natural numbers less than 400 can I assemble if the numbers do not repeat? - Probability 6186
Grandma used to cook sheep and cottage cheese pies together. There were 30 made from sheep cheese and 5 fewer made from cottage cheese. Juraj took the first one and got 6 brownies and 3 curds. What is the probability that my first pie will not be bronze? - Exactly 5803
There are 15 black and 20 white balls in Destiny. How many ways can six balls be drawn to have exactly two whites between them? - How many
How many double-digit numbers greater than 30 can we create from digits 0, 1, 2, 3, 4, and 5? We cannot repeat numbers in a two-digit number.
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