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

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Step 1

1 of 4

The described experiment is equivalent to:

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

Outcome space SS contains every combination of cards.

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

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

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

in the chapter 1.4. it is shown that the number of four card combinations of 52 different cards is (524)=S\binom{52}{4}=|S|

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