In the card game Bridge, 4 players in teams of two play against each other. One pack of cards is dealt out among them, so that each player has 13 cards. Point values can be assigned to the picture cards - Ace is 4, King 3, Queen 2, and Jack 1, so there are 40 points in the deck.
An important part of Bridge is to make contracts (or bids) for a certain number of tricks, and a good indicator of your success is how many points you and your partner have combined.
What is the probability that one team will have at least enough for:
a) a "game contract" - 26 points? (bidding to take most of the tricks)
b) a "small slam" - 33 points? (bidding to take all but one of the tricks)
c) a "grand slam" - 37 points? (bidding to take all the tricks)
As bonus questions, what are the odds that just your hand will be:
d) a Yarborough (0 point hand with highest card a 10)
e) a Royal Yarborough (0 point hand with no card higher than a 9)
f) a "game hand" (a hand with 26 or more points)?