probability 52 card problem

A standard deck of 52 cards is shuffled, and each of 3 people are asked to select a card at

random from the deck. Each time a card is selected, it is returned to the deck and reshuffled.

What is the probability that

(a) all 3 people select different cards?

(b) exactly one of the 3 people selects a heart?

(c) the first person selects a heart or the last person selects an ace?

heres what im tinking... let me know if this seens logical

a) (1/52)(1/51)(1/50)

b)(1/52) (1/52) (1/4)

c)