How many five – card hands are possible, which consist of three red cards and two black cards?

Answer 1

There are 26 cards which are red, that is 2-A, hearts and diamonds.
There are also 26 cards which are black, that is 2-A, clubs and spades.

There are C(26, 3) - "26 choose 3" - ways to choose 3 red cards of 26. C(26, 3) = 26*25*24/(3*2*1) = 2600

There are C(26, 2) - "26 choose 2" - ways to choose 2 black cards of 26. C(26, 2) = 26*25/(2*1) = 325.

The fundamental counting principle says multiplying these two together will give the number of possibilities: 2600 * 325 = 845000

Answer 2

Hello

There are 26 red cards so we want 3 at a time or 26C3.

There are 26 black cards so we want 2 at a time or 26C2

So we have 26C3*26C2= 2600*325 = 845000

Hope This Helps!!

Answer 3

eight since there are only 26 red cards and after eight hands, there aren't three red cards left to complete the ninth hand and meet your criteria.