Hello All,

Please help me solve this problem:

How many ways are there to choose 4 cards of different suits and different values from a deck of 52 cards?

Thank you,

Ashwin Kumar D P, Bangalore, India

- October 23rd 2009, 08:10 AMashwinkumardpChoosing 4 cards of different suits and different values from a deck of 52 cards.
Hello All,

Please help me solve this problem:

How many ways are there to choose 4 cards of different suits and different values from a deck of 52 cards?

Thank you,

Ashwin Kumar D P, Bangalore, India - October 23rd 2009, 09:08 AMSoroban
Hello, Ashwin!

I had to "draw a picture" to understand this one . . .

Quote:

How many ways are there to choose 4 cards of different suits

and different values from a deck of 52 cards?

. .

The first card can be any of the 52 cards.

. . Suppose it is

Then these choices remain for the second card:

. .

There are 36 choices for the second card.

Suppose the second card is

Then these choices remain for the third card:

. .

There are 22 choices for the third card.

Suppose the third card is

Then these choices remain for the fourth card:

. .

There are 10 choices for the fourth card.

Disgarding the order in which the four cards are drawn,

. . there are: . such 4-card hands.

- October 2nd 2010, 03:09 PMRelmiw
I understand where the 52, 36, 22, and 10 came from, but why divide by 4!? could anyone describe it in a way that makes sense?