# Combinatorics - math word problems

1. 2nd class combinations From how many elements you can create 4560 combinations of the second class?
2. Bits, bytes Calculate how many different numbers can be encoded in 16-bit binary word?
3. Party At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party?
4. Kids How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
5. Lines In how many points will intersect 14 different lines, where no two are parallel?
6. Commitee A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?
7. Hockey players After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
8. Lottery The lottery is 60000 elk in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
9. Monty Hall Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
10. Numbers How many different 3 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2?
11. Area codes How many 6 digit area codes are possible if the first number can't be zero?
12. School trip The class has 19 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms. (Each room has its unique number)
13. Toys 3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?
14. Family What is the probability that a family with 7 childrens have: exactly 5 girls? 7 girls and 0 boys? Consider the birth probability of a girl is 48.69% and boy 51.31%.
15. 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?
16. Three digits number How many are three-digit integers such that in they no digit repeats?
17. 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?
18. Bulbs The probability that the bulb can operate 4000 hours is 0.3. What is the probability that exactly one of eight bulbs can operate 4000 hours?
19. Cars plates How many different licence plates can country have, given that they use 3 letters followed by 3 digits?
20. Chess How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?

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