In a deck of cards there are 4 suits of 13 cards each. If the face value of the aces is defined as 1 and the jack, queen, and king are 11, 12, and 13 respectively, then:
1)
What is the probability of drawing 2 cards from the deck whose face values add up to 13?
What is the probability of drawing 3 cards whose face values add up to 13?
Is there a way to generalize this to $k$ cards adding up to $n$?
2)
What is the probability of drawing 3 cards that are 3 consecutive Fibonacci numbers?
What is the probability of drawing 4 cards that are 4 consecutive Fibonacci numbers?
(For eg.: ace, ace, 2, 3 or 3, 5, 8, 13. But the order in which they are drawn is not important!)
Is there a way to generalize this to $k$ cards that are $k$ consecutive Fibonacci numbers?