Mathematics Control Part 3

Verification work on discipline "Mathematics" (Part 3), "the number of questions - 10.


Task 1. From the city A to city B are 5 roads in and out of the city in the city with - three roads. How many paths that pass through in the lead from A to C?


Task 2. There are 6 pairs of gloves in various sizes. In how many ways you can choose the one glove on his left hand, and one - to the right so that the gloves were selected in different sizes?


Task 3. Five girls and three boys playing in small towns. In how many ways they can be broken into two teams of 4 people, if each team must have at least one boy?


Task 4. In conjunction railcar has two opposing sofas for 5 seats on each. Of the 10 passengers on the four compartments are willing to sit face to the engine, 3 - back to the engine, and the rest is indifferent to sit. How many ways can accommodate passengers with regard to their desires?


Task 5. The post office selling postcards of ten species in unlimited amounts. In how many ways you can buy 12 cards?


Task 6. The competition in gymnastics involved nearly 10 people at the same degree of skill. Three judges must be independent of each other to renumber them in order of their success in the competition, according to the judges. The winner is the one who first called at least two judges. In what proportion of all possible cases, the winner will be defined fission?


Task 7. An urn lie 10 tokens with numbers 1, 2, 3, ..., 10. Of her, choosing the token is removed 3. In how many cases the amount of numbers written on them not less than 9?


Task 8. Man has 6 friends, and within 20 days invites you to the three of them, so that the company has never repeated. In how many ways can he do it?


Task 9. outing went 92 people. Sausage sandwich took 47 people with cheese - 38 people, with ham - 42 people, with cheese and sausage - 28 people, and sausage and ham - 31 people, and with cheese and ham - 26 people. All three types of sandwiches took 25 people, and a few people instead of sandwiches brought with them cakes. How many people have brought the pies?


Task 10. Find the solution of the problem, which consists in determining the maximum value of the function: