There is a deck of 52 cards (13 hearts, 13 spades, 13 diamonds, 13 clovers). You and your friend both pick two cards at random. Do not consider the order in which cards are picked.

(a) How many outcomes are in the sample space?

(b) Calculate the probability that you get two hearts?

(c) Given that you have got two hearts, what is the conditional probability that you friend has got two clovers?

(d) What is the probability that you get two hearts and your friend get two clovers?

(e) What is the probability that you and your friend get the same shape? (that is, all four cards are heart, spade, diamond or clover)