Hello, white_cap!
I "talked" my way through it . . .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.