Q.Three cards are drawn successively, without replacement, from a well-shuffled deck of $52$ playing cards. Find the probability that all three cards drawn are jacks.

[!TLDR] Chain rule: $\tfrac{4}{52}\times\tfrac{3}{51}\times\tfrac{2}{50}$. [!ANSWER] $P(\text{all three jacks})=\dfrac{1}{5525}$.

There are $4$ jacks. $P(\text{1st jack})=\tfrac{4}{52}$. Given the first is a jack, $P(\text{2nd jack})=\tfrac{3}{51}$ ($3$ jacks left in $51$ cards). Given both are jacks, $P(\text{3rd jack})=\tfrac{2}{50}$. By the chain rule, $P=\tfrac{4}{52}\times\tfrac{3}{51}\times\tfrac{2}{50}=\dfrac{24}{132600}=\dfrac{1}{5525}$. [!ANSWER] $P(\text{all three jacks})=\dfrac{1}{5525}$.

Multiply three successive conditional probabilities, reducing both the jack count and the total card count by $1$ after each draw.

Using the same fraction $\tfrac{4}{52}$ three times (as if drawing with replacement) instead of updating the counts is a very common error for this problem type.