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Math Exercises: Variations, Permutations, Combinations

 

 

 

 

1. If we reduce the number of elements by two, the number of permutations reduces thirty times. Find the number of elements.

 

2. From how many elements we can create six times more variations without repetition with choose 2 as variations without repetition with choose 3 ?

 

3. If the number of elements x is increased by two, the number of variations without repetition from x elements choose 3 increases by 294. Find the number of elements.

 

4. How many three-digit natural numbers can be assembled from the digits 2, 3, 4, 5, 6, 7, if the digits are not repeated ? How many of these numbers are divisible by five ?

 

5. The registration number of the vehicle consists of two letters, three numbers and two letters. How many registration numbers can we form if we use 25 letters ?

 

6. How many different six-digit numbers can be constructed from the digits 1, 2, 3 ?

 

7. There are places where in the buses are used tickets with nine squares numbered from 1 to 9. When a passenger boards the bus, he inserts the ticket into the machine which makes little holes through three or four of the squares. How many different ways exists for the perforation of the bus ticket ?

 

8. In how many ways can sit around a circular table 12 people, if for each of them is not important the place where they sit, but just who is his neighbour from the left and from the right side ?

 

9. In how many ways can in the cinema sit next to each other seven friends A, B, C, D, E, F, G, if buddy B sits on the seat no. 4 and buddy G sits on the seat no. 2 ?

 

10. There is 24 boys and 15 girls in a dance circle. How many different pairs can be formed if the dancing couple is always a pair of girl-boy ?

 

11. There are 20 students in the class. In how many ways can we choose a couple for a weekly service ?

 

12. How many players participated in the tournament in table tennis, where 21 matches was played and each player played with each other exactly once ?

 

13. There are 20 girls and 15 boys in the class. How many different five-member teams could be formed if each team should be composed of three girls and two boys ?

 

14. The hockey team has 20 players: 13 attackers, 5 defenders and 2 goalkeepers. How many different formations a trainer can form if the ice formation is to have 3 attackers, 2 defenders and 1 goalkeeper ?

 

15. A teacher has 20 arithmetic and 30 geometric math exercises. There should be two arithmetic and three geometric tasks on the test. How many options has the teacher to create the test ?

 

16. A 6-member group, in which should be exactly 3 women, has to be created from 7 men and 4 women. Find out how many possibilities do we have to create such a group.

 

17. A teacher has to choose three students from the class 3A and two students from the class 3B to the recitation competition. There are 22 students in the 3A and 17 students in the 3B class. How many possible choices does she have ?

 

18. How many possibilities of seating arrangements exists here for friends A, B, C, D, E, where buddy A sits next to the buddy C ?

 

19. Latin alphabet has 26 letters. How many different 6-letter "words" could be formed out of it ?

 

20. The registration number of the vehicle consists of three letters and three numbers. How many registration numbers can we form if we use 28 letters ?

 

21. Five girls, from which two are sisters, are standing in one line in the sports hall. How many ways there exists to set the girls so that the sisters were standing next to each other ?

 

22. Calculate the number of possible different configurations of ten books on the shelf, where four detective novels are to be next to each other.

 

23. How many ways a teacher has to choose three students from among 12 to carry the mathematical books ?

 

24. How many natural numbers divisible by five smaller than 8,000 exist, if they are made out of the digits 0, 1, 2, 5, 7, 9 ?

 

25. How many possible ways there is for 12 visitors of the cinema to sit in one row, if each of the six married couples wants to sit next to each other ?

 

26. How many natural numbers smaller than 301 exist, if they are made out of the digits 0, 1, 2, 3, 6, 7 ?

 

27. In how many ways can we put on the tailor thread 3 red, 4 blue and 5 yellow beads ?

 

28. From how many elements we can create 15 combinations without repetition with choose 2 ?

 

29. From how many elements we can assemble 120 permutations without repetition ?

 

30. From how many elements we can create 504 variations without repetition with choose 3 ?

 

 

 

 

 

 

You might be also interested in:

- Binomial Theorem

- Probability

- Factorials and Combinatorial Expressions

- Combinatorial Equations and Inequalities

 

 
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