Question

What is the probability that a five-card poker hand contains a royal flush, that is, the 10, jack, queen, king, and ace of one suit?

Answer 1

Answer:

0.00000154 or 0.154 x 10^-6

Step-by-step explanation:

P (Royal Flush) = Number of ways to get a Royal Flush / Number of possible  5 card hands

Because there are 4 suits (Spades, Hearts, Clubs, Diamonds), the possible ways to get a royal flush are as follows

1) Spades (10,J,K,Q,A)

2) Hearts (10,J,K,Q,A)

3) Clubs  (10,J,K,Q,A)

4) Diamonds (10,J,K,Q,A)

Hence there are 4 ways to get a Royal Flush (i.e numerator)

In order to find the number of 5 card hands, we know that a full deck as 52 cards, and we want to pick 5 cards from the deck of 52 and order does not matter. Hence

Number of possible 5 card hands = $=^{52} C_{5}$

Hence P(Royal Flush) = 4 / $=^{52} C_{5}$  

= 0.00000154 or 0.154 x 10^-6