Combinatorics - math word problems - page 48 of 51
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: 1005
- Distribute 70244
We have to distribute the keys to the safe among four people so that no two of them can open the safe but in such a way that any three can open the safe. How many minimum keys do we need? How to divide them? How many minimum locks must be on the safe? All - Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube? - Playing cards
From 32 playing cards containing eight red cards, we choose four cards. What is the probability that just two will be red? - Probability 69914
During the exam, each student receives 30 different questions, from which he chooses 3 at random. To pass the exam, he needs to be able to answer two correctly. What is the probability that a student will pass if he mastered 70% of the questions (70% of t
- Lines
How many points will intersect 14 different lines where no two are parallel? - Probability 7627
In the monitored group of people, 8% are ill with the flu. One hundred people from this group were examined. What is the probability that at most 5 of them will be sick with the flu? (round to 3 decimal places) - Probability 38041
Seven women and 3 men work in one office. According to the new regulation, reducing the number of employees by three is necessary. In a random sample of employees, what is the probability that they will be fired: a. One woman and two men b. At least one w - Intersections 26781
A rectangular grid consists of two mutually perpendicular systems of parallel lines with a distance of 2. We throw a circle with a diameter of 1 on this plane. Calculate the probability that this circle: a) overlaps one of the straight lines; b) do any of - Manufacturer 80810
The manufacturer indicates that the germination rate of the pepper seeds is 68%. What is the probability that a) out of ten seeds sown, at least 8 will germinate? b) will at most 3 sprouts out of ten seeds be sown?
- 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 - Manufacturer 24801
With a repeat check, five hundred of the series of products are to be inspected. The manufacturer guarantees 2% scrap for a given production. Determine the probability of scraps among the 500 products reviewed between 12 and 20. - Probability - tickets
What is the probability when you have 25 tickets in 5000 that you do not win the first (one) prize? - Covid-19
Data showed that 22% of people in a small town were infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents were infected. - 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?
- Test
The teacher prepared a test with ten questions. The student can choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers all correctly. c - Probability 80723
According to long-term statistics, a biathlete has a shooting success rate of 72%. a) what is the probability that 4 targets will be hit on one item (5 shots). b) what is the probability that fewer than 4 targets are hit on one item (5 shots)? - Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high-temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because precisely one of t - Determined 16233
How many lines are determined by 5 points if three lie in one line? - Students and exam
In a certain college, accounting is one of the courses; among the accounting students, 60% are male. Among the male students, 75% passed the exams, while among the females, 50% failed. (a) present this using a probability tree diagram (b) determine the pr
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