Question

if you draw a 5-card hand from a standard deck of playing cards, how many hands could contain exactly 4 cards from the same suit?

Answer 1

wait a little confused. does this mean what is the probability you get exactly 4 cards of the same suit?

Answer 2

watchmath do you understand this question?

Answer 3

perhaps the answer is
\[\dbinom{13}{4}\times \dbinom{39}{1}\times 4\]?

Answer 4

i don't really know how to intemperate "if you draw a 5-card hand"..."how many hands"

Answer 5

that is what i'm trying to figure out!

Answer 6

well maybe it means how many possible hand have 4 of one suit and two of another. if so, lets start with clubs. you need 4 clubs and 1 non club. the number of ways to get 4 clubs is \[\dbinom{13}{4}\] and the number of ways you can choose one non-club is
\[\dbinom{39}{1}\]

Answer 7

then we do the same for each other suit hence multiply by 4

Answer 8

yes.....

Answer 9

my theory is 4(13 C4* 39C1)

Answer 10

that is what i wrote so it looks good to me

Answer 11

4*13*11*5*39

Answer 12

Thank you very much !!

Answer 13

welcome