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Practice — Maths 11 • Combinatorics

Combinatorics problems
Difficulty: ★★☆
1852 • Задача 1, вариант 1

At Chorsu Bazaar, 7 types of skullcaps and 6 types of belts are sold. In how many ways can one buy a gift consisting of one skullcap and one belt?

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Combinatorics problems
Difficulty: ★★☆
1853 • Задача 1, вариант 2

In the café “Oshkhona”, in the morning one can order a “Light Breakfast” set consisting of one drink (tea, coffee, ayran, compote) and one pastry (samsa, katlama, or bugirsok). How many different such sets are possible?

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Combinatorics problems
Difficulty: ★★☆
1854 • Задача 1, вариант 3

At the market in Samarkand, the following dried fruits are sold: raisins, dried apricots, uryuk, prunes, dried apples, and pears. In how many ways can one buy a set of two different types of dried fruits?

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Combinatorics problems
Difficulty: ★★☆
1855 • Задача 1, вариант 4

When buying a “Damas” car, one can choose the body color (white, silver, black, blue) and the seat upholstery material — fabric or leather. How many different “color + seats” configurations are possible in total?

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Combinatorics problems
Difficulty: ★★☆
1856 • Задача 1, вариант 5

A university librarian is arranging a special exhibition dedicated to Alisher Navoi with rare editions of his works: “Khamsa”, “Divan”, “Confusion of the Righteous”, and a collection of lyrics. The books need to be placed in a row on one shelf. In how many ways can the librarian do this?

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Combinatorics problems
Difficulty: ★★☆
1857 • Задача 1, вариант 6

Several friends went on a mountain hike to Chimgan: Alisher, Bekhzod, Dilshod, Said, Farkhod, and Sherzod. To pitch a tent, two of them must be chosen. In how many ways can this pair be chosen?

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Combinatorics problems
Difficulty: ★★☆
1858 • Задача 1, вариант 7

In the canteen of an institute in Tashkent, a business lunch consists of a first course (shurpa, mastava, or lagman) and a second course (kabob, manti, or kuk-samsa). How many different business lunch options can be formed?

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Combinatorics problems
Difficulty: ★★☆
1859 • Задача 1, вариант 8

The locker code in the “Timur” sports complex consists of two digits. The first digit is even, the second is odd. How many such codes can be created?

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Combinatorics problems
Difficulty: ★★☆
1860 • Задача 1, вариант 9

A workshop in Khiva sells suzane with 7 different patterns and in 2 sizes (large and small). Each pattern is available in both sizes. How many different suzane can be bought in total?

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Combinatorics problems
Difficulty: ★★☆
1861 • Задача 1, вариант 10

A passenger remembered that the three-digit number of the “Tashkent–Bukhara” bus started with the digit 2, and the other two digits were different odd digits. How many such numbers exist?

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Combinatorics problems
Difficulty: ★★☆
1862 • Задача 1, вариант 11

In a school volleyball tournament, 4 teams took part. Each team played two matches against every other team. How many matches were played in total?

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Combinatorics problems
Difficulty: ★★☆
1863 • Задача 1, вариант 12

The Aliyev family in full composition (father, mother, son, and daughter) asked a photographer to take a commemorative photo in front of the Registan in Samarkand. The photographer suggested that they stand in one row. In how many different ways can the family members stand for the photo, if all of them must be in the picture?

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Combinatorics problems
Difficulty: ★★☆
1864 • Задача 1, вариант 13

When buying a smartphone in the “Samarqand Darvoza” store, one can choose a model (7 options) and a body color (black, gray, blue, pink). Each model is available in all colors. How many phone choices are there in total for the buyer?

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Combinatorics problems
Difficulty: ★★☆
1865 • Задача 1, вариант 14

The Wi-Fi password in the Ulugbek madrasa consists of two symbols: the first is a letter (У, Л, Г, Б, Е, К), and the second is one of the digits of Ulugbek’s birth year: 1394. How many different passwords are possible?

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Combinatorics problems
Difficulty: ★★☆
1866 • Задача 1, вариант 15

In the folk dance ensemble “Lazgi”, a male soloist and his female partner must be chosen for a new dance. The auditions were attended by the boys (Alisher, Rustam, and Bakhodir) and the girls (Aziza, Zukhra, Nigora, Sabina, Yulduz). In how many ways can such a leading dance pair be formed?

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Combinatorics problems
Difficulty: ★★☆
1867 • Задача 1, вариант 16

For the Navruz celebration, two different fruit trees are to be planted in the schoolyard. The nursery has saplings of the following types: apple, pear, quince, apricot (uryuk), cherry, persimmon, and plum. In how many ways can two different types of trees be chosen for planting?

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