AMC 10,

question 4.27, 4.28 and 4.30. (help I dont understand)

Suppose you have the numbers

{0,1,2,3,4,5}{0,1,2,3,4,5}. How many 66-digit numbers can be formed with 11 next to 00 or 22? (Use each number exactly once.) Caution: 012345012345 is not a 66 digit number so be careful!

There are objects in a bag defined by its color (red, blue) and shape (cube, ball). There are a total of 6060 objects in the bag, none of which are blue cubes. 3030 of the objects are red and 4040 of the objects are balls. How many blue balls must be painted red in order to have a 20%20% increase in total number of red balls in the bag?

Suppose you give out the 55 (current) ASOIAF books to 33 of your friends. Each friend gets at least one book. How many ways an you give out the books? Do the calculation using PIE and directly using cases.