Question

If you have a deck of 24 cards and 4 of those are kings and 4 are queens, what is the probability of being dealt a hand of 5 cards with neither any kings nor any queens?

Answer 1

I was thinking that you would have a sample space of (24 choose 5) and the size of the event would be (16 choose 5) since you leave out the king and queens. Then you can just find the probability by doing (16 choose 5)/(24 choose 5)

Answer 2

Well, how many possibilities are there?

Answer 3

you have a couple ways to proceed

Answer 4

one it to say, first card is not a king or queen, second card is not a king or queen, third card is not a king or queen etc
that would give you
\[\frac{16}{24}\times \frac{15}{23}\times \frac{14}{22}\times \frac{13}{21}\times \frac{12}{20} \]

Answer 5

second way is to say there are \(\binom{24}{5}\) possible 5 card hands, and
\(\binom{16}{5}\) ways to pick t he not kings or queens and you compute
\[\frac{\dbinom{16}{5}}{\dbinom{24}{5}}\]

Answer 6

oh you are right, i didn't see your answer

Answer 7

yeah, I am working on a multiple part problem and I ran into a problem later on. I just wanted to be sure that my thinking was correct for this part. Thanks for your help!

Answer 8

yw