GUJCET 2026 Math Paper

Concept:These are dependent events because cards are drawn without replacement, so multiply their probabilities.Explanation:There are $4$ kings in a deck of $52$ cards.Probability that the first card is a king is $\frac{4}{52}=\frac{1}{13}$.After one king is removed, $3$ kings remain in $51$ cards.Probability that the second card is also a king is $\frac{3}{51}=\frac{1}{17}$.After two kings are removed, $50$ cards remain and there are still $4$ aces.Probability that the third card is an ace is $\frac{4}{50}=\frac{2}{25}$.Required probability is $\frac{4}{52}\times\frac{3}{51}\times\frac{4}{50}$.This equals $\frac{1}{13}\times\frac{1}{17}\times\frac{2}{25}=\frac{2}{5525}$.Answer:$\frac{2}{5525}$