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

you are being asked how many ways there are to choose 2 out of 13 and 3 out of 13
the number of ways to choose 2 out of 13 is called "thirteen choose two"
written as \(\binom{13}{2}\) or sometimes \(_{13}C_2\)
have you seen these?

Answer 2

okay yes on the calculator it would be 13 nCr 2?

Answer 3

then press enter and thats the correct answer?

Answer 4

you can use a calculator, i am not sure how
you can do this as well \[\binom{13}{2}=\frac{13\times 12}{2}\]

Answer 5

cancel first, multiply last

Answer 6

then similarly \[\binom{13}{3}=\frac{13\times 12\times 11}{3\times 2}\]
when you get those two, multiply them

Answer 7

if you really want to use a calculator, do this
http://www.wolframalpha.com/input/?i=(13+choose+2)(13+choose+3)

Answer 8

yes and you get 286

Answer 9

for which?

Answer 10

13 x 12x11 over 3 x2

Answer 11

ok i believe you
then you still have to multiply the two numbers

Answer 12

and get 22308

Answer 13

?

Answer 14

thank you for the help!!!