how many different ways could you choose 6 cards from a standard deck of 52 cards, if you must have atleast one card from each suit, and order does not matter.

I got 8682544, is this correct?

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- October 22nd 2007, 09:28 PMwhite_capcombinations: possibly really easy?
how many different ways could you choose 6 cards from a standard deck of 52 cards, if you must have atleast one card from each suit, and order does not matter.

I got 8682544, is this correct? - October 23rd 2007, 04:56 AMPlato
- October 23rd 2007, 05:43 PMSoroban
Hello, white_cap!

Quote:

How many different ways could you choose 6 cards from a standard deck of 52 cards,

if you must have at least one card from each suit, and order does not matter.

I got 8682544, is this correct? . . . . I got the same answer!

We choose six cards, and all four suits are represented.

There are two distributions of suits.

(1) There is 1 of the first suit, 1 of the second suit, 1 of the third suit,

. . and 3 of the fourth suit: .

There are: .4 choices for the "triple" suit.

Then there are: . ways to choose the cards.

Hence: there are: . ways to draw

(2) There is 1 of the first suit, 1 of the second suit, 2 of the third suit,

. . and 2 of the fourth suit: .

There are: . to select the suits.

Then there are: . ways to choose the cards.

Hence, there are: . ways to draw

Therefore, there is a total of: . ways.