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

Answer:

P = 0.000004

Explanation:

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

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

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:

$P=\frac{1}{270725}=0.000004$

So, the answer is P = 0.000004