Question

All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards, two are drawn randomly, without replacement, then probability of drawing a pair (same denominations) is

• A. $\frac{1}{13}$
• B. $\frac{1}{78}$
• C. $\frac{2}{39}$
• D. $\frac{4}{13}$

Answer 1

The correct option is A $\frac{1}{13}$

Remaining cards $=40$

Total ways of drawing two cards $={}^{40}{C}_2$

Favourable ways $=10\times {}^4{C}_2$

Probability $=\frac{10\times 6}{{}^{40}{C}_2}=\frac{1}{13}$