# Combinatorics - math word problems

1. Eight blocks Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
2. Three-digit numbers How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
3. Three-digit How many three-digit natural numbers is greater than 321 if no digit in number repeated?
4. Combinatorics The city has 7 fountains. Works only 6. How many options are there that can squirt ?
5. Bulbs In the box are 6 bulbs with power 75 W, 14 bulbs with power 40 W and 15 with 60 W. Calculate probability that a randomly selected bulb is:
6. Hockey Hockey match ended 8:2. How many different matches could be?
7. Shooters In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.
8. Committees How many different committees of 6 people can be formed from a class of 30 students?
9. Trainings The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kova
10. Three digits number From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
11. The dice What is the probability of events that if we throw a dice is rolled less than 6?
12. Hearts 5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
13. Olympics In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
14. Candies In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
15. Lion or virgin We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
16. Chess How many different ways can initiate a game of chess (first pass)?
17. A three-digit numbers Determine the total number of positive three-digit numbers that contain a digit 6.
18. Probabilities If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
19. Dices throws What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
20. Weekly service In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?

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