MEI Higher mathematics control 10 questions

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Assignment 1. From the city of A to B 5 roads lead, and from the city of B in the city of S - three roads. How many paths passing through B lead from A to C?
Task 2. There are 6 pairs of gloves of different sizes. How many ways can you choose from them one glove on the left hand and one on the right so that the selected gloves are of different sizes?
Task 3. Five girls and three boys play in the towns. How many ways can they split into two teams of 4 people, if there is at least one young man in each team?
Task 4. In the compartment of the railway car there are two opposite sofas with 5 seats each. Of the 10 passengers of this compartment, four wish to sit facing the locomotive, 3 - back to the locomotive, and the rest do not care how to sit. How many ways can accommodate passengers according to their desires?
Task 5. In the post office cards of ten kinds are sold in unlimited quantities. How many ways can I buy 12 cards?
Task 6. In the gymnastics competition, 10 people are practically the same in degree of skill. Three judges should independently renumber them in an order reflecting their success in the competition, according to the judges. The winner is the one who will be called first by at least two judges. In what proportion of all possible cases will the winner be determined?
Task 7. In the urn there are 10 tokens with the numbers 1, 2, 3, ..., 10. Out of it, not choosing, take out 3 tokens. In how many cases the sum of the numbers written on them is not less than 9?
Task 8. A person has 6 friends and within 20 days invites 3 of them to him so that the company never repeats. How many ways can he do this?
Task 9. 92 people went on a country outing. Sandwiches with sausage were taken by 47 people, with cheese - 38 people, with ham - 42 people, and with cheese and sausage - 28 people, and with sausage and ham - 31 people, and with cheese and with ham - 26 people. All three types of sandwiches were taken by 25 people, and several people took pies with sandwiches instead of sandwiches. How many people took pies with them?
Task 10. Find the solution of the problem, which consists in determining the maximum value of the function:
 
under conditions

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