[Discrete maths] Permutations and combinations

Question

How many ways can n books be placed on k distinguishable shelves 
a. if no two books are the same ,and the positions of the books on the shelves does not matter?
b. if no two books are the same,and the positions of the books on the shelves matter?

Answer 1

for first part i think it should be k^(n)

for 2d part here k*(k+1)*(k+2)*..........(k+n-1)

: Break this into n tasks, placing each book separately. Start with the sequence 1,2,3,4.......k  to represent the shelves. Represent the books by bi, i = 1, 2, ..., n. Place b1 to the right of one of the terms in 1, 2, 3, 4............. Then successively place b2, b3, ..., and b12.)

There are k ways to place b1, (k+1)  ways to place b2, ..., (k+n-1) ways to place bn. correct if i am wrong here