Question

$12$ people are asked questions in succession in a random order and exactly $3$ out of $12$ people know the answer. The probability that the $6^{t h}$ person asked is the $2^{n d}$ person to know the answer, is

• A. $\frac{10}{21}$
• B. $\frac{3}{22}$
• C. $\frac{7}{11}$
• D. $\frac{5}{12}$

Answer 1

Answer: (B)

$6^{t h}$ Person asked is the $2^{n d}$ person to know the answer
$\Rightarrow $ In the first five people there must be exactly one person who knows the answer
Required probability $=\frac{^{9} C_{4} \times ^{3} C_{1}}{^{12} C_{5}}\times \frac{2}{7}$
$=\frac{9 \times 8 \times 7 \times 6 \times 120 \times 3}{24 \times 12 \times 11 \times 10 \times 9 \times 8}\times \frac{2}{7}=\frac{3}{22}$