Question

Five cards are selected from a 52-card deck for a poker hand. a. How many simple events are in the sample space? b. A royal flush is a hand that contains the A, K, Q, J, and 10, all in the same suit. How many ways are there to get a royal flush? c. What is the probability of being dealt a royal flush? Please, please, please explain and not just give the answer or formula.

Answer #1

**Solution:-**

**a) Total number of combinations of different hands =
2,598,960**

Total number of cards = 52

Number of cards to be selected = 5

**Total number of combinations of different hands =
^{52}C_{5} = 2,598,960**

**b) The number of hands for royal flush = 4**

There are total four suits in 52-card deck, hence number of hands for royal flush = 4

**c) The probability of being dealt a royal flush =
0.00000153908**

The probability of being dealt a royal flush = 4/2,598,960

**The probability of being dealt a royal flush =
0.00000153908**

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