Combinatorics - math word problems

  1. Possible combinations - word
    dices2 How many ways can the letters F, A, I, R be arranged?
  2. Pairs of socks
    probability Ferdinand has twelve pairs of socks, one sock is leaky. What is the probability of putting on a leaky sock?
  3. Twenty-five
    prime How many three-digit natural numbers are divisible by 25?
  4. Auto-tuning
    tv During auto-tuning, the TV searched for 25 channels, four of which were music. The channels are stored in the TV's memory in random order. Express the percentage of the event that the music channel will be saved first.
  5. Beads
    koralky2 How many ways can we thread 4 red, 5 blue, and 6 yellow beads onto a thread?
  6. Cube construction
    222cube A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
  7. Ball bearings
    normal_d One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w
  8. Boys and girls
    dancers There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them?
  9. Year 2020
    eq222 The four-digit number divided by 2020 gives a result of 1, **. (Can not be in form 1,*0. ) Write all the options.
  10. Two groups
    skola 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?
  11. Balls
    gulky From the bag with numbered balls (numbers 1,2,3,. ..20) we pick one ball. What is the probability of choosing a number containing 1?
  12. Graduation party
    dancers There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected.
  13. Records
    binomial_1 Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
  14. Genetic disease
    flu One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
  15. Dice and coin
    dice A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
  16. Probability of malaria
    malaria A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patie
  17. Today in school
    skola There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
  18. One three
    dice We throw two dice. What is the probability that max one three falls?
  19. Holidays with grandmam
    saty We have packed three T-shirts - white, red, orange and five pants - blue, green, black, pink and yellow. How many days can we spend with the old mother if we put on a different combination of clothes every day?
  20. Lathe
    sustruh 95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



Would you like to compute count of combinations?