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Question

# Involve a deck of $52$ cards.A poker hand consists of five cards.$\textbf{a.}\hspace{10pt}\text{Find the total number of possible five-card poker hands.}$$\textbf{b.}\hspace{10pt}\text{Find the number of ways in which four aces can be selected.}$$\textbf{c.}\hspace{10pt}\text{Find the number of ways in which one king can be selected.}$$\textbf{d.}\hspace{10pt}\text{Use the Fundamental Counting Principle and your answers from parts (b) and (c) to find the number of ways getting four aces and one king.}$$\textbf{e.}\hspace{10pt}\text{Find the probability of getting a poker hand of four aces and one king.}$

Solution

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The situation describes combination because the order in which the cards are selected is not important. We use the combination formula:

$_nC_r=\dfrac{n!}{(n-r)!r!}$

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