# Combinatorial number - high school - practice problems

#### Number of problems found: 139

- Honored students

Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them? - A license

A license plate has 3 letters followed by 4 numbers. Repeats are not allowed for the letters, but they are for the numbers. If they are issued at random, what is the probability that the 3 letters are in alphabetical order and the 3 numbers are consecutiv - School parliament

There are 18 boys and 14 girls in the class. In how many ways can 3 representatives be elected to the school parliament, if these are to be: a) the boys themselves b) one boy and two girls - Soccer teams

Have to organize soccer teams. There are 3 age groups. How many different ways can you organize teams of ten for each age group? Is this a permutation or combination? - Alopecia

Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most two men suffer from alopecia. - Ten persons

Ten persons, each person makes a hand to each person. How many hands were given? - Playing cards

From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red? - Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Deficiencies

During the hygienic inspection in 2000 mass caterers, deficiencies were found in 300 establishments. What is the probability that deficiencies in a maximum of 3 devices will be found during the inspection of 10 devices? - Hazard game

In the Sportka hazard game, 6 numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess 5 numbers correctly) b) the third prize (we guess 4 numbers correctly)? - Tournament

How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the overall winner of the tournament? - Wagons

We have six wagons, two white, two blue, and two red. We assemble trains from them, wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train, because I don't know any different. How many di - Six questions test

There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What - Research in school

For particular research in high school, four pupils are to be selected from a class with 30 pupils. Calculate the number of all possible results of the select and further calculate the number of all possible results, if it depends on the order in which th - Probability of failures

In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than one failure among the 100 selected products if we return the selected products to the file after the check. - All use computer

It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs. - Table and chairs

Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chair between them if people choose their place completely at random? - Divide

How many different ways can three people divide 7 pears and 5 apples? - Sick days

In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. .. what is the probability an employee will use 17 OR MORE sick days in a year? - Fruits

In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?

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See also our combinations calculator. Combinatorial number - practice problems. Examples for secondary school students.