Question

Three cards are drawn successively without replacement from a pack of $52$ well shuffled cards. The probability that first two cards are queens and the third card is a king, is

• A. $\frac{4}{52}\times\frac{4}{51} \times \frac{4}{50}$
• B. $\frac{4}{52}\times\frac{2}{51} \times \frac{1}{50}$
• C. $\frac{4}{52}\times\frac{3}{51} \times \frac{3}{50}$
• D. $\frac{4}{52}\times\frac{3}{51} \times \frac{4}{50}$

Answer 1

Answer: (D)

$\frac{4}{52}\times\frac{3}{51} \times \frac{4}{50}$

Answer 2

Probability when first two cards are queens out of $52$ cards $=\frac{^{4}C_{1}}{^{52}C_{1}}\times\frac{^{3}C_{1}}{^{51}C_{1}}$ Probability when third card is king out of $50$ cards $=\frac{^{4}C_{1}}{^{50}C_{1}}$ Hence, the required probability $=\frac{^{4}C_{1}\times^{3}C_{1}\times^{4}C_{1}}{^{52}C_{1}\times^{51}C_{1}\times^{50}C_{1}}$ $=\frac{4}{52}\times\frac{3}{51}\times\frac{4}{50}$