Question

If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are queens.The probability is(Round to six decimal places as needed.)

Answer 1

P = 0.000004

Step-by-step explanation:

The number of ways or combinations to select 4 cards from 52 cards can be calculated using the following equation:

`\begin{gathered} \text{nCx}=(n!)/(x!(n-x)!) \\ 52C4=(52!)/(4!(52-4)!)=(52!)/(4!\cdot48!)=270,725 \end{gathered}`

It means that there are 270,725 ways to select 4 cards out of 52.

Additionally, there are only 4 queens in the deck, so there is only one possibility where the 4 cards are queens. So, the probability that all 4 cards are queens is:

`P=(1)/(270725)=0.000004`

So, the answer is P = 0.000004