Combinatorial number - practice problems
Number of problems found: 296
- 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? - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - A ferry
A ferry with a capacity of 10 people takes a group of 13 men and 7 women across a river. Find the number of ways in which the group may be taken across the if all women go on the first group. - Two dice 3
Two dice are thrown together. What is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other dice? 2/3 9/36 12/36 11/18
- Student examination
How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - 52 cards
A hand of five cards is dealt from a pack of 52 playing cards. How many different hands can be dealt that contain three aces? - 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? - Manufacturing company It is established by the production manager of a manufacturing company that 2 out of every 20 units of a particular product are faulty. In a particular production hour, 8 units of the product were produced. Determine the probability that: (1) none of them
- Containers
One in eight containers is temporarily misplaced. A random sample of 12 containers is selected. What is the probability that 6 of these containers will be temporarily misplaced?
- Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people. - Bulb lifespan
The probability that the bulb will burn for more than 800 hours is 0.2. There are 3 light bulbs in the hallway. What is the probability that after 800 hours, at least one will be lit? - Playmakers + coach
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - Probability 83308 There are 10 parts in the box, and 3 of them are defective. Let's choose 4 components at random. What is the probability that it will be among them a) 0 defective, b) just one defective component, c) just two defective components, d) exactly 4 defective c
- Probability 83267 The cube has 6 blue, 8 red, and 10 green balls. The player randomly draws 3 balls. Determine the probability that he draws balls of the same color.
- Possibilities 82372
A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed? - Competition 82310
In the shooting competition, each shooter fires 5 shots. Shooter Muška will hit the target with one shot with a probability of 60%. What is the probability that he hits at least once out of five shots? - Possibilities 81788 The ring consists of 4 beads. There are 5 different colors of beads in the package. How many possibilities are there to create one ring, and can the colors repeat?
- Participated 81728 The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated.
- Probability 81685 There are 49 products in the box, of which only 6 are good. We will randomly draw 6 products from them. What is the probability that at least four of the products drawn are good?
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