# Combinatorics - examples - page 3

1. Subsets
How many are all subsets of set ??
2. Insurance
The owner of the house is insured against natural disasters and pays 0.04% annually of the value of house 77 Eur. Calculate the value of the house. Calculate the probability of disaster, if you know that 48% of the insurance is to pay damages.
3. Party
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
4. 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
5. Pizza
A school survey found that 10 out of 11 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?
6. Kids
How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
7. Lines
In how many points will intersect 14 different lines, where no two are parallel?
8. 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?
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. Lottery
The lottery is 60000 elk in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
11. Area codes
How many 6 digit area codes are possible if the first number can't be zero?
12. 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?
13. School trip
Class has 17 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 1× 3-bed and 2× 4-bed rooms. (Each room has its own unique number)
14. Numbers
How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6?
15. 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?
16. 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%.
17. Three digits number
How many are three-digit integers such that in they no digit repeats?
18. 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?
19. 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?
20. 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?

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