# Combinatorics - examples - page 4

1. Three digits number How many are three-digit integers such that in they no digit repeats?
2. Components In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
3. Combi-triangle On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
4. Bulbs The probability that the bulb can operate 5000 hours is 0.16. What is the probability that exactly one of three bulbs can operate 5000 hours?
5. Cars plates How many different licence plates can country have, given that they use 3 letters followed by 3 digits?
6. Chess How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?
7. Seven-segmet Lenka is amused that he punched a calculator (seven-segment display) numbers and used only digits 2 to 9. Some numbers have the property that their image in the axial or central symmetry was again give some number. Determine the maximum number of three-d
8. Elections In elections candidate 10 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes. The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I
10. Examination The class is 21 students. How many ways can choose two to examination?
11. Raffle How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.
12. Math logic There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w
13. Friends in cinema 5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
14. Logik game Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numbe
15. Digits How many natural numbers greater than 4000 which are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers less than 4000 and the numbers can be repeated?
16. Cinema How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
17. Tournament Determine how many ways can be chosen two representatives from 34 students to school tournament.
18. Peak Uphill leads 2 paths and 1 lift. a) How many options back and forth are there? b) How many options to get there and back by not same path are there? c) How many options back and forth are there that we go at least once a lift?
19. Seating rules In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
20. Medals In how many ways can be divided gold, silver and bronze medal among 21 contestant?

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