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14.Probability
normal
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
$\frac{4}{{13}}$
Solution
Remaing cards $=40$
Total ways of drawing two cards $=\,\,^{40} \mathrm{C}_{2}$
favaroble ways $=10 \times\,^{4} \mathrm{C}_{2}$
Probability $=\frac{10 \times 6}{^{40} \mathrm{C}_{2}}=\frac{10 \times 6 \times 2}{40 \times 39}=\frac{1}{13}$
Standard 11
Mathematics
