# Five cards are drawn at random from an ordinary deck of 52 cards. ?

Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red cards and three black cards?

Relevance

There are

26C2 = 26! / (24! * 2!)

= 26 * 25 / 2 = 325 ways to draw two red cards.

There are

26C3 = 26! / (23! * 3!)

= 26 * 25 * 24 / (3 * 2) = 1300 ways to draw three black cards.

325 * 1300 = 422,500 ways to draw two red and three black cards.

• a. sixty 5,780 strategies There are 26 red playing cards once you commence, and each and each and every time you draw one, there is one a lot less. There are 5! orders in which an same set of 5 playing cards would properly be drawn. (26 x 25 x 24 x 23 x 22) / (5 x 4 x 3 x 2 x a million) = 7,893,600 / 120 = 65780

• red cards = 26 of them

black cards = 26 of them

ways of drawing 2 red cards = 26*25 since there can't be any repeats.

ways of drawing 3 black cards = 26*25*24

ways of drawing 2 red AND 3 black

(26*25) * (26*25*24)

This assumes that drawing a red 10 of hearts first and then a red 10 of diamonds second counts as one way and then drawing them in reverse counts as well as another way. If this is not the case, the Samwise's answer is correct