Martians play poker with a deck of 64 cards. There are 9 "suits" corresponding to the 9 planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune, Pluto, which the Martians still recognize as a planet). Each "suit" has 7 cards, so that a typical card is E6 (the 6 of the Earth suit). A Martian poker hand consists of nine cards. A Martian full house consists of 5 cards with one number, and 4 cards with a different number (e.g., a typical Martian full house consists of 5 2's and 4 6's; this is (obviously) a different hand than 4 2's and 5 6's).
(a) How many Martian poker hands are there?
(b) How many Martian poker hands are Martian full houses?
(c) If a Martian poker hand is dealt at random, what is the probability that it is a Martian full house.