SOLUTION: How may FIVE card poker hands are there?

Question 168922: How may FIVE card poker hands are there?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How may FIVE card poker hands are there?
----------------------
The 1st card can be one of 52, the 2nd will be 1 out of 51, etc, so we get 52*51*50*49*48 = 311,875,200.
But, drawing 3 4 5 6 7 is the same hand as drawing 3 7 5 6 4 (the same 5 cards drawn in a different order), so we have to divide by 5*4*3*2*1 = 5! = 120.
That gives the number of different hands = 2,598,960.
-------------------------
This is based on the assumption that the same card in a different suit makes a different hand. For example, a full house with 3 Kings, the 10 of Hearts and the 10 of Spades, is viewed as different from a hand with any of the 5 cards exchanged for the same card of a different suit. It has no effect on where it's a winning or losing hand in poker.
Whether this assumption is valid is not specified.

RELATED QUESTIONS
How many FIVE card poker hands contain all RED... (answered by josmiceli)

An ordinary deck of cards consists of four suits: clubs, diamonds, hearts and spades, of... (answered by stanbon)

Suppose you play poker but the dealer shuffles two 52 card decks together and deals. How... (answered by Edwin McCravy)

A poker hand consists of five cards from a standard deck of 52. How many poker hands are... (answered by robertb)

A poker hand consists of five cards dealt from a deck of 52. How many diferent poker... (answered by checkley71)

In a 5-card poker game a player is dealt 5 cards. How many poker hands are possible for... (answered by stanbon)

how many five-poker hands consisting of the following distribution are there? a- aflush... (answered by stanbon)

From a standard 52-card deck, how many 5-card poker hands can be dealt consisting of each (answered by stanbon)