# Combinatorics - practice problems

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: 961

- Probability 82362

If we roll one die, what is the probability of rolling a number other than 1? - Choices 82334

There are 15 black and 15 white balls in an opaque bag. Elenka took one ball out of the bag three times. what choices of the three balls could she choose? - Three coins

In a game of chance where three coins are tossed, a player wins if two heads and a tail come up. What are the chances of this occurring? - How many 32

How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - How many 31

How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students? - A single

A single, standard number cube is tossed. What is the probability of getting a number greater than 3? - Pet store 2

A pet store is having a prize giveaway. The spinner shows the type of toy a customer can win for their pet. If a customer spins the spinner and it lands on a cat, they will win a free cat toy. If the spinner is spun 540 times throughout the day, about how - Probability 81842

In an opaque bag are chips with numbers from 1 to 20. What is the probability that we will draw a chip with a number less than 16? - Representative 81580

The chess club has 5 members, including two girls. The circle leader wants to determine by lot which member will represent the circle at the representative tournament. What is the probability that a girl will be drawn? - Assume 2

Assume you are working with a standard six-sided die. What is the probability of rolling the die once and obtaining a 5 and then rolling the die again and obtaining a 2? (input 3 numbers after the decimal, do not round). Report probability as a proportion - A fair 2

A fair die is thrown two times. What is the probability that the sum of the score is almost 8? - The probability 2

The probability that an adult possesses a credit card is 0.71. A researcher selects two adults at random. The probability (rounded to three decimal places) that the first adult possesses a credit card and the second adult does not possess a credit card is - Simultaneously 80530

The product has a 10% probability of an appearance defect, a 6% probability of a functional deficiency, and a 3% probability of both defects simultaneously. Are the random events A - the product has an appearance defect and B - the product has a functiona - Probability 80394

We have 10 red and 10 white balls. We will take 5 white. What is the probability of picking a white ball? - Natural numbers

Determine the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, and 8 occur at most once each. - Four-digit 79614

Determine the number of all four-digit natural numbers in decimal notation in which the digit 0 is not present, and each of the remaining nine numbers occurs at most once. - Determine 79604

In the shoe cabinet, there is one pair each of boots, sandals, tennis shoes, and brown and black ankle boots. Determine how many ways one right shoe and one left shoe can be chosen from among them that do not belong together. - Dishes

Out of 5 different dishes, the HOD is to test at least three different dishes before scoring the students. How many ways can he choose the dishes? - Five brown

Five brown eye contracts, seven green pairs, and four blue pairs. What's the probability Gianna will randomly select a brown or green pair? - A fair coin

A fair coin is tossed twice. Write down the set of possible outcomes. What is the probability of obtaining it? I. Exactly one head ii. No head

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