1. How many 5 cards hand can be drawn (without replacement) from the standard deck of 52 cards so that hand contains 2 distinct pairs of cards and one dissimilar one?
2. How many integer solutions are there to equation w+x+y+z=12 if solutions are non-negative? positive?
3. How many 4-letter words can be formed from words:
i) ANOTHER
ii) FLUFFY
iii) WILLOW
4. How many ways can 15 indistingushable marbles be distributed into 6 distingushable bins if all bins should have at least one marble assigned to them?
5. Brian requires to put 12 distingushable school books away. 4 of them are science, 5 of them are math and remaining three are computer books. How many ways can Brian arrange book if:
i) All books are to be placed single shelf in any order?
ii) All books of same subject should be grouped together, all on one self?
iii) Each book can be placed on any of three different shelves in any order?
iv) All books of same subject should be grouped together on the separate shelf, but every subject may be placed on any of three shelves?
v) Every subject is on the different shelf and books within every subject are arranged in alphabetical order?