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Practice — Maths 9 • Elements of combinatorics

Combinatorics
Difficulty: ★☆☆
1548 • Задача 1, вариант 1

A shop sells 5 types of rulers and 4 types of erasers. In how many ways can you buy a set consisting of one ruler and one eraser?

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Combinatorics
Difficulty: ★☆☆
1549 • Задача 1, вариант 2

A shop sells 4 types of balloons: red, blue, yellow, and green. In how many ways can you buy a set of two balloons of different colours?

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Combinatorics
Difficulty: ★☆☆
1550 • Задача 1, вариант 3

Before noon, a café offers a “Light Breakfast” set consisting of one drink and one pastry: a bun, a vatrushka, or a pie. The café has 7 different drinks. How many different “Light Breakfast” sets are possible?

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Combinatorics
Difficulty: ★☆☆
1551 • Задача 1, вариант 4

When buying a new car model, you can choose the body colour — 5 options — and the wheel type — alloy or stamped. How many different “colour + wheels” configurations are there?

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Combinatorics
Difficulty: ★☆☆
1552 • Задача 1, вариант 5

In a pizzeria, you can order a Margherita pizza with two extra toppings chosen from five offered toppings (olives, mushrooms, peppers, ham, pear). How many different pizzas can be ordered?

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Combinatorics
Difficulty: ★☆☆
1553 • Задача 1, вариант 6

Six people went on a hike. In how many ways can two of them be chosen to prepare dinner?

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Combinatorics
Difficulty: ★☆☆
1554 • Задача 1, вариант 7

In a cafeteria, a business lunch consists of a first course (borscht, noodle soup, or solyanka) and a second course (cutlet, fish, or vegetable stew). How many different business lunch options can be formed?

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Combinatorics
Difficulty: ★☆☆
1555 • Задача 1, вариант 8

A suitcase code consists of two digits. The first digit is odd, and the second is even. How many such codes are there?

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Combinatorics
Difficulty: ★☆☆
1556 • Задача 1, вариант 9

To assemble a robot, you need to choose one board and one корпус. The set contains 6 different boards and 3 types of cases (small, medium, large). How many different robots can be assembled by choosing one option of each element?

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Combinatorics
Difficulty: ★☆☆
1557 • Задача 1, вариант 10

In the final of a school chess tournament, 4 players took part. Each player played every other player 4 games (twice with white and twice with black). How many games were played in total?

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Combinatorics
Difficulty: ★☆☆
1558 • Задача 1, вариант 11

A store sells T-shirts in 8 different colours and 3 sizes (S, M, L). Each colour is available in all sizes. How many different T-shirt variants are there in the store?

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Combinatorics
Difficulty: ★☆☆
1559 • Задача 1, вариант 12

A passenger remembered that the three-digit taxi number began with the digit 7, and the other two digits were different even digits. How many such numbers are there?

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Combinatorics
Difficulty: ★☆☆
1560 • Задача 1, вариант 13

In a pizzeria, you can order a “sausage and cheese” pizza. There are 7 types of cheese and 2 types of sausage to choose from. How many different “sausage and cheese” pizzas can be made?

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Combinatorics
Difficulty: ★☆☆
1561 • Задача 1, вариант 14

Five volleyball teams took part in a tournament. Each team played one match with every other team. How many matches were played?

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Combinatorics
Difficulty: ★☆☆
1562 • Задача 1, вариант 15

Before noon, a café offers a “Good Morning!” set consisting of a drink and one samsa: chicken, meat, potato, or pumpkin. The café has 4 different drinks. How many different “Good Morning!” sets are possible?

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Combinatorics
Difficulty: ★☆☆
1563 • Задача 1, вариант 16

An entry key card has a two-symbol code: the first symbol is a letter (K, L, M), and the second is a digit (1, 2, 3, 4). How many different keys can there be?

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