Combinatorial number - practice problems - page 7 of 16
Number of problems found: 307
- Honored students
Of the 25 students in the class, ten are honored. How many ways can we choose five students from them if there are to be exactly two honors between them? - Defective 35831
Among the 24 products, seven are defective. How many ways can we choose to check a) 7 products so that they are all good b) 7 products so that they are all defective c) 3 good and two defective products? - A license
A license plate has
three letters followed by four 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 three letters are in alphabetical order and the three number - School parliament
There are 18 boys and 14 girls in the class. In how many ways can three representatives be elected to the school parliament if these are to be: a) the boys themselves b) one boy and two girls - Two-element combinations
Write all two-element combinations from elements a, b, c, and d. - Soccer teams
Have to organize soccer teams. There are three age groups. How many different ways can you organize ten teams for each age group? Is this a permutation or combination? - Competition 33041
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe?
- Probability 32951
Determine the probability that when drawing three cards from a complete set of 32 marriage cards, it will be the same acorns or the kings themselves. - Alopecia
Medical literature indicates that 45% of men suffer from alopecia. For a random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most, two men suffer from alopecia. - Guests - party
There are 13 guests at each other's party. How many clicks will you hear? - Ten persons
Ten persons, each person, make a hand to each person. How many hands were given? - 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 30421
There are 25 students in the class, 12 of whom are not ready for math. There are five students in the math class. What is the probability of at least 3 being math-ready? - Probability 30311
There are 200 components in the production batch, of which 26 have a plus deviation from the nominal value. Calculate the probability that none of the 10 products selected will have a positive variance if we make selections without repetition - Probability 30271 The probability of an adverse drug reaction is 2.1%. How many people need to be prescribed for one patient to experience side effects with a chance of 90%?
- 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
The hygienic inspection of 2000 mass caterers found deficiencies in 300 establishments. What is the probability that flaws in a maximum of 3 devices will be found during the inspection of 10 devices? - Hazard game
In the Sportka hazard game, six numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess five numbers correctly) b) the third prize (we guess four numbers correctly)? - Punishment 26851
Alena, Ivana, Edo, Filip, and Martin came late to school. As a punishment, two will water flowers all over the school after class, and the other three will clean up the classroom. The class teacher couldn't decide who to send to water the flowers, so Juro - 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 tournament's overall winner?
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