Question

you are dealt 5 cards out of a 52 card deck. what is the probability you are dealt 2 kings and 2 sevens?

Answer 1

you tell that dealt 5 cards, but ur question dealt 2 (K) and 2 (7)'s, where is the rest one ? :)

Answer 2

it could be any of the remaining cards

Answer 3

i keep getting (4 choose 2)(4 choose 2)(44 choose 1)/(52 choose 2)

Answer 4

two kings, two sevens, and a card other can K or 7
\[\frac{\displaystyle \binom{4}{2}\binom{4}{2}{\binom{44}{1}}}{\displaystyle \binom{52}{5}}\]

Answer 5

why (52 choose 2). shouldn't you choose 5 cards among 52?

Answer 6

yep sorry thats what i ment

Answer 7

this is what i used on wolfram
http://www.wolframalpha.com/input/?i=probability+2+kings+and+2+queens

Answer 8

so it keeps showing that the numerator should be 612

Answer 9

KKQQE <- 4/52 * 3/51 * 4/50 * 3/49 * 44/48
KKQEQ <- 4/52 * 3/51 * 4/50 * 44/49 * 3/48

So for every permutation you'll get
(4*4*3*3*44)/(52*52*50*49*48)
total no. of permutations = 5!/2! 2! = 30

Even my logic yield the same ans as what we obtained here and not wolfram's. hmm

Answer 10

alright see i have gone though this many times. maybe wolfram is taking something into consideration that im not but its alright. I think im gunna just go with what i originally had and it should be ok. Thank you for your help!

Answer 11

wolfram appears to be doing some crazy stuff