5 cards are extracted simultaneously from a deck of 32 shown in the picture: a bunch of this kind is made up of 8 cards for each of the four suits (hearts, diamonds, spades and clubs): 7,8,9,10, Jack, Queen, King, Ace.
5 cards are extracted simultaneously from a standard deck of 32 cards (8 cards for each of the four suits (hearts, diamonds, spades and clubs): 7,8,9,10, Jack, Queen, King, Ace).
How many different ways can you extract 5 cards containing exactly 3 of hearts and exactly 2 cards king?
How many different ways can you extract 5 cards containing exactly 3 hearts and exactly 2 kings?
The answer of my book is: 1428 different ways
, I am not able to achieve this.
first case
The two kings are not either of their hearts.
Disp (3,2) = 6$\binom{3}{2} = 6$ possibilities ==> The hearts cards that remain are EIGHT !! But the king of hearts must be excluded, otherwise the kings extracts become three !!! So are 7 !!!
paintings Spades paintings Flowers spades Paintings spades Flowers flower Paintings Spades flowers
6 * disp (7, 3) = 1260$$6 \times \binom{7}{3} = 1260$$
second case
One of the two king of hearts.
hearts Spades hearts Paintings Flowers hearts Hearts spades Diamonds Hearts Hearts flowers
6 always possible ==> The hearts cards that remain are SEVEN because it lacks the king of hearts
6 * disp (7, 2) = 6 * 7 * 6 = 252 Google Traduttore per il Business:Translator ToolkitTraduttore di siti webStrumento a supporto dell'export$$6 \times \binom{7}{2} = 6 \cdot 7 \cdot 6 = 252$$
1260 + 252 = 1512 and not 1428But $1260 + 252 = 1512 \ne 1428$
What am I doing in the wrong way?
Thank you very much for considering my request.
