# Combinatorics - examples - page 5

1. Medals
In how many ways can be divided gold, silver and bronze medal among 21 contestant?
2. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
3. The camp
At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
4. Digits
Write the smallest and largest 1-digit number.
5. Circles
How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
6. Variations 3rd class
From how many elements we can create 13,800 variations 3rd class without repeating?
7. Raffle
In the pool is numbers from 1 to 115. What is the probability that a randomly selected number is not a prime number?
8. 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
9. Three-digit numbers
How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?
10. Three-digit
How many three-digit natural numbers is greater than 321 if no digit in number repeated?
11. Combinatorics
The city has 7 fountains. Works only 6. How many options are there that can squirt ?
12. 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:
13. Hockey
Hockey match ended 8:2. How many different matches could be?
14. 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.
15. Committees
How many different committees of 6 people can be formed from a class of 30 students?
16. 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
17. 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?
18. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
19. 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?
20. Olympics
In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.

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