Question

A 5-card hand is dealt from a deck of 52 cards. What is the probability that 3 cards are queens and two are kings?

Answer 1

qqqkk has 5!/(3! 2!) ways of getting pulled

4P3 queens, 4P2 kings = 4.3.2.4.3; out of 52P5 outcomes

Answer 2

so i see it as:\[10*\frac{4.5.3.4.3}{52.51.50.49.48}\]simplify as needed

Answer 3

I'm a little confused on how you did it. Also the answers around
0.00000923

Answer 4

got a typo in th enumerator ...

Answer 5

i added up all the possible ways to pull 3 queens and 2 kings:

qqqkk1
qqkqk2
qkqqk3
kqqqk4
qqkkq5
qkqkq6
kqqkq7
qkkqq8
kqkqq9
kkqqq10

the probability of something happening is the sum of all the ways it can happen

as we pull the cards we have 4queens to pick from, then 3, then 2

we have 4 kings to pick from , then 3 giving us the respective probabilities for a single permuations

Answer 6

4P3 = 4.3.2
4P2 = 4.3

10 ways to pull them, and 52 pick 5 different ways to pull 5 cards out of 52

Answer 7

\[10*\frac{4.3.2.4.3}{52.51.50.49.48}\]
\[\frac{4.3.2.4.3}{52.51.5.49.48}\]
\[\frac{3.2.4.3}{52.51.5.49.12}\]
\[\frac{3.2}{52.51.5.49}\]
\[\frac{3}{26.51.5.49}\]
\[\frac{1}{26.17.5.49}\]

Answer 8

http://www.wolframalpha.com/input/?i=1%2F%2826*17*5*49%29

9.2344630... × 10^-6

Answer 9

Thank you!

Answer 10

youre welcomme