Question

From a deck of 52 cards, how many 5-card hands can be formed with at least 3 diamonds?

Answer 1

there are 13 diamonds divided by 3 gives 4 possible decks with at least 3 diamonds

Answer 2

wut.

Answer 3

A lot.

What have you tried?

Answer 4

im not sure, i feel like it starts off with \[? nCr 5 \]?

Answer 5

do you know how many hands if there are exactly 3 diamonds?

Answer 6

:/ no...

Answer 7

5 hand?

Answer 8

how many ways can you choose 3 cards from 13?

Answer 9

so 13 Cr 3?

Answer 10

o wait

Answer 11

i meant 13 nCr 3

Answer 12

drop the r

\[\Large_{13}C_3\]

Answer 13

ok

how many cards are not diamonds?

Answer 14

i don't know

Answer 15

a card is a diamond or it is not. you have 52 total cards and 13 of them are diamonds

Answer 16

39

Answer 17

ok

Answer 18

how many ways can you choose the remaining 2 card from the 39?

Answer 19

38?

Answer 20

so 39 * 38 * 37

Answer 21

no

Answer 22

this is again a combination

Answer 23

you are CHOOSING 2 cards from 39

Answer 24

what where did the 2 come from

Answer 25

you are picking a 5 card hand. 3 are diamonds...thus the other 2 cards must not be diamonds

Answer 26

oh psh right :/

Answer 27

um so after 2, 37's left

Answer 28

I don't care how many are left after you pick 2. We need to know how many ways we can pick the 2 cards from the 39

Answer 29

it is the same exact idea we used to choose the 3 diamonds

Answer 30

39 C 2

Answer 31

and then multiply it with 13 C 3

Answer 32

yes

Answer 33

but that is not the final answer

Answer 34

because they are asking for AT LEAST 3 diamonds we need to do this tow more times. one with 4 diamonds and one with 5 diamonds

Answer 35

*two

Answer 36

N(at least 3 diamonds)
=N(get exactly 3 diamonds)+N(get exactly 4 diamonds)+N(get exactly 5 diamonds)

Answer 37

13 C 4 * 38 C 1; 13 C 5 * 37 C 0

Answer 38

oh

Answer 39

almost

Answer 40

there are always 39 cards that are not diamonds

Answer 41

LOL shet

Answer 42

ok

Answer 43

so it's 13 C 4 * 39 C 1; 13 C 5 * 39 C 0

Answer 44

yes...so what is the final answer?

Answer 45

211926?

Answer 46

no

Answer 47

oh no

Answer 48

crap

Answer 49

one sec

Answer 50

241098

Answer 51

yes

Answer 52

LOL THANK YOU SO MUCH

Answer 53

no problem