Combinatorial analysis for computing

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Combinatorial analysis for computing
Exercises
1) A lot of 100 items contains K defective items, where K < 100. M items are selected at random and tested, where M < 100.
 a) What is the probability that N are found defective, where N < K, M ? 
b) A selection is accepted if 1 or fewer of the M items are defective. What is the probability that the selection is accepted?
2) A small community consists of 10 women, each of them has 3 children. If one woman and one of her children are to be chosen as the mother-child of the year, how many different choices are possible?
3) A class of probability theory consists of 6 male and 4 female students. Assume no two students obtain the same score. 
a) If all students are ranked according to their performance how many different rankings are possible? 
b) If the male and female students are ranked among themselves how many different rankings are possible?
4) A chess tournament has 4 competitors of which 3 are Russian and 1 is American. If the tournament result lists just the nationalities of the players in the order in which they placed, how many outcomes are possible?
5) Consider the grid of points on the board. Starting from A you can go one step up or one step right at each move, until you reach B. 
a) How many different paths from A to B are possible? 
b) How many different paths are there from A to B that go through C?