A standard deck of 52 cards consists of 4 suites (hearts,
diamonds, spades and clubs) each containing 13 different values
(Ace, 2, 3, …, 10, J, Q, K).
If you draw some number of cards at random you might or might
not have a pair (two cards with the same value) or three cards all
of the same suit. However, if you draw enough cards, you will be
guaranteed to have these. For the following, find the smallest
number of cards you would need to draw to be guaranteed having the
specified cards. Provide a proof to support
your answer:
Three of a kind (for example, three 7's).
A flush of five cards (for example, five hearts).