"What is the chance of getting first two kings, then two que

[stats_help81]

"What is the chance of getting first two kings, then two queens, then an ace, and then finally either a king or a gueen or an ace?"

 

[soroban]

Hello, stats_help81!

What is the chance of getting first two Kings, then two Queens, then an Ace,
and then finally either a King or a Queen or an Ace?

I assume that six cards are drawn without replacement from a standard deck of cards.


\(\displaystyle \text{Probability that the first card is a King: }\:\frac{4}{52}\)

\(\displaystyle \text{Probability that the second card is a King: }\:\frac{3}{51}\)

\(\displaystyle \text{Probability that the third card is a Queen: }\:\frac{4}{50}\)

\(\displaystyle \text{Probability that the fourth card is a Queen: }\:\frac{3}{49}\)

\(\displaystyle \text{Probability that the fifth car is an Ace; }\:\frac{4}{48}\)

\(\displaystyle \text{Probability that the sixth card is a King or Queen or Ace: }\:\frac{7}{47}\)
[There are 2 Kings, 2 Queens and 3 Aces left in the deck.]


\(\displaystyle \text{Answer: }\;\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{4}{50}\cdot\frac{3}{49}\cdot\frac{4}{48}\cdot\frac{7}{47} \;=\;\frac{1}{3,635,450}\)

 

[stats_help81]

Thank you!