In how many ways can a dozen books be placed on four distinguishable shelves
- if the books are indistinguishable copies of the same title?
- if no two books are the same, and the positions of the books on the shelves matter? [Hint: Break this into $12$ tasks, placing each book separately. Start with the sequence $1, 2, 3, 4$ to represent the shelves. Represent the books by $b_{i}, i = 1, 2,\dots, 12.$ Place $b_{1}$ to the right of one of the terms in $1, 2, 3, 4.$ Then successively place $b_{2}, b_{3},\dots, \text{and }\:b_{12}.]$