Combinatorial number + reason - math problems
Number of problems found: 55
- 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
- Two-element combinations
Write all two-element combinations from elements a, b, c, d.
- 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?
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?
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
- 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?
How many different ways can three people divide 7 pears and 5 apples?
In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?
In the flower shop they sell roses, tulips and daffodils. How many different bouquets of 5 flowers can we made?
- Twelve flowers
A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these 4 types of flowers would be possible?
- Pairs of socks
Ferdinand has twelve pairs of socks, and one sock is leaky. What is the probability of putting on a leaky sock?
- Two groups
The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?
- Graduation party
There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
- Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
- Three numbers
We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
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