# Combinatorics - examples - page 6

1. 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? ?
2. Weekly service
In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
3. Teams
How many ways can divide 16 players into two teams of 8 member?
4. travel agency
Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
5. Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
6. Green - Red
We have 5 bags. Each consist one green and 2 red balls. From each we pull just one ball. What is the probability that we doesn't pull any green ball?
7. 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
8. Cards
How many ways can give away 32 playing cards to 4 player?
9. MATES
In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
10. Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
11. Hockey game
In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
Peter and Franta threw to the basket. Each had 20 attempts. Peter scored thirteen and twelve Franta. Give them success in percentage.
13. Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
14. Calculation of CN
Calculate: ?
15. Medicine
We test medicine on 6 patients. For all drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work?
16. Pupils
Four pupils is going via dark hall. Start at one side and have to get to the other side for 17 minutes. They have only one lamp for the trip. The corridor is narrow, they can therefore go up two pupils at a time and go at the slower speed. Each pupil went.
17. Football league
In the football league is 16 teams. How many different sequence of results may occur at the end of the competition?
18. Combinations
How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
19. Trinity
How many different triads can be selected from the group 38 students?
20. Sum on dice
We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?

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