# Will you fold?

**Discrete Mathematics**Level 5

*hand*is an

*unordered*set of five cards. The following is the ranking of poker hands. In case an hand belongs to both possible classification of hands,

*only the higher rank is considered*.

\(1\). **Royal Flush:** The set of best cards from 10 to A all in the same suit.

A♦ K♦ Q♦ J♦ 10♦

\(2.\) **Straight Flush:** Five Cards of Consecutive ranks of the same suit.

Q♣ J♣ 10♣ 9♣ 8♣

\(3.\) **Four of a Kind:** Four Cards of the same rank.

9♣ 9♠ 9♦ 9♥ J♥

\(4.\) **Full House:** Two Cards of the same rank and three other cards of a similar rank.

6♠ 6♥ 6♦ A♠ A♣

\(5.\) **Flush:** Five Cards all in the same suit

K♥ Q♥ 9♥ 5♥ 4♥

\(6.\) **Straight:** Five Cards of consecutive ranks

10♣ 9♦ 8♥ 7♣ 6♠.

\(7.\) **Three of a kind:** Three cards of the same rank

2♦ 2♠ 2♣ K♠ 6♥

\(8.\) **Two Pairs:** Two pairs of cards each consisting of a pair of matching ranked cards.

10♠ 10♣ 4♠ 4♥ 8♥

\(9.\) **One Pair:** A pair of cards of the same rank

4♥ 4♠ K♠ 10♦ 5♠

If a hand does not match any of the above, it can be called a **high-card** or a **no-pair**.

How many such **high-card** hands exist provided you're choosing from a standard deck?