Combinatorics - practice problems - page 3 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: 999
- A disease
A disease affects 10% of the individuals in a population, and a sample of 100 people was selected from the population. What is the probability of finding the disease in at least 15 people? - Defect rate
A manufacturing machine has a 3% defect rate. If 9 items are chosen randomly, what is the probability that at least one will have a defect? - Grandchildren 83113
The grandfather bought 10 rubbers for 10 grandchildren. In the bag were 3 blue, 2 green and the rest red. Hansel would like blue gum. What is the probability that Janek will draw a blue rubber if 2 cousins have already drawn it before him and drawn blue a - 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? - 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? - 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 - Menu choice
In a Jollibee, you have a menu choice of C1, C2, and C3. For dessert, you have a choice of ice cream and mango peach. How many different options do you have? - Competition 73174
There are 10 students in the class, of which 8 are girls and two are boys. We want to select three for the competition. What is the probability that they will be: a) 2 girls and 1 boy b) 1 girl and 2 boys c) 3 girls d) 3 boys e) at least 2 girls - 20 balls
20 colored balls in a bag: Four red Seven green Nine yellow What is the probability of picking a yellow ball? - Four-digit 73114
How many four-digit numbers can we assemble from the digits 2, 6, 3, 5, 1, and 9 if the numerals in the number cannot be repeated? - T-shirts 73074
Dušan has 8 T-shirts and three pairs of shorts in his closet. How many ways can he dress for school?
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