immanuelv 5 years ago 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?

1. anonymous

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

2. anonymous

watchmath do you understand this question?

3. anonymous

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

4. anonymous

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

5. immanuelv

that is what i'm trying to figure out!

6. anonymous

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 $\dbinom{39}{1}$

7. anonymous

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

8. immanuelv

yes.....

9. immanuelv

my theory is 4(13 C4* 39C1)

10. anonymous

that is what i wrote so it looks good to me

11. anonymous

4*13*11*5*39

12. immanuelv

Thank you very much !!

13. anonymous

welcome