#### Question

An ordinary deck of 52 cards is shuffled. What is the probability that the top four cards have (a) different denominations? (b) different suits?

#### Solution

Verified#### Step 1

1 of 4The described experiment is equivalent to:

$\textit{Experiment: Four random cards are drawn from a standard 52 card deck}$

Outcome space $S$ contains every combination of cards.

If all events in $S$ are considered equally likely, probability of event $A\subseteq S$ is:

$\begin{equation*} P(A)=\dfrac{|A|}{|S|} \end{equation*}$

where $|X|$ denotes the number of elements in $X$

in the chapter 1.4. it is shown that the number of four card combinations of 52 different cards is $\binom{52}{4}=|S|$

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