4. Assume that you are playing poker with a standard 52-card deck of playing cards and you are dealt 5 cards. Calculate the probability that you were dealt the following hands. Use any method you wish to perform the calculations (permutations, combinations, conditional probability, brute force counting, etc.). Note that for a test, I will accept answers that are left using combinations, but for this assignment please find the numerical values of the probabilities, to put everything in context.

a) only one pair (ex: AA58K)

b) two pairs (ex: AAKK4)

c) three of a kind (ex: AAA47)

d) straight (5 cards in sequence, using any suit - exclude the cases when all 5 cards are of the same suit) (ex: 45678)

e) flush (5 cards of the same suit - exclude the cases when the cards are in sequence)

f) full house (three of a kind and a pair) (ex: AAAKK)

g) four of a kind (ex: AAAAK)

h) straight flush (5 cards in sequence of the same suit)

Hint: Do part (h) before parts (d) or (e).