Question

How many five-card hands chosen from a standard deck contain two hearts and three spades?
Hint: In a standard deck of cards, diamonds and hearts are different suits. In this situation, they are different categories of cards. There are 13 cards in each suit. (If necessary, type the number with no commas or spaces. For example: 258963)

Answer 1

c(13,2) = 13!/(2!(13-2)!) = 78

c(13,3) = 13!/(3!(13-3)!) = 286

286 x 78 = 22308

Answer 2

The number of five-card hands chosen from a standard deck contain two hearts and three spades are 22308.

What is the combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

The number of cards chosen,

$\\^{13}C_2=\dfrac{13!}{3!(13 - 2 )!}=\dfrac{13\times 12}{2}=78$

$\\^{13}C_3=\dfrac{13!}{3!(13 - 3 )!}=\dfrac{13\times 12 \times 11}{6}=286$

The number of the cards are,

N = 286 x 78 = 22308

Therefore, the number of five-card hands chosen from a standard deck containing two hearts and three spades is 22308.

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