Concept explainers
In a single deal of 5 cards from a standard 52-card deck, what is the probability of being dealt 5 clubs?

To calculate:The probability of drawing 5 clubs in a single deal of 5 cards drawn from a standard deck of 52 cards.
Answer to Problem 1RE
The probability of drawing 5 clubs is 0.0005 approximately.
Explanation of Solution
Calculation:
Let E be the event of drawing 5 clubs. The total number of outcomes is n(S)=C525.
The number of club cards in a deck is 13 out of which 5 are drawn.
Compute the number of ways in which 5 club cards are selected.
n(E)=C135
Compute the probability of event E by dividing the number of outcomes of an event by number of outcomes of sample space.
P(E)=n(E)n(S)=C135C525=13!5!8!52!5!47!=13!5!8!×5!47!52!
Further solve as,
P(E)=13×12×11×10×9×8!5!8!×5!47!52×51×50×49×48×47!=11×34×17×5×49×4=3366640≈0.0005
Therefore, the probability of drawing 5 clubs is 0.0005 approximately.
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