Question

What is the probability that the first $2$ draws from a pack of cards are clubs and the third is a spade?
(Assume all cards are drawn without replacement)

• A. $\frac{2,028}{132,600}$
• B. $\frac{38}{132,600}$
• C. $\frac{1,716}{132,600}$
• D. $\frac{2,028}{140,608}$
• E. $\frac{1,716}{140,608}$

Answer 1

The correct option is A $\frac{2,028}{132,600}$

Probability of drawing a club from a pack of $52$ cards is $\frac{13}{52}$
Now there are $51$ cards ($12$ clubs)
Probability of drawing another club is $\frac{12}{51}$
Now there are $50$ cards ($11$ clubs)
Probability of drawing a spade is $\frac{13}{50}$
Therefore, the combined probability is $\frac{13}{52}\times \frac{12}{51}\times \frac{13}{50}=\frac{2028}{132600}$