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 $6^{th}$ person asked is the $2^{nd}$ 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)

$6^{th}$ Person asked is the $2^{nd}$ person to know the answer
$\Rightarrow$ In the first five people there must be exactly one person who knows the answer
Required probability $=\frac{{}^9{C}_4{\times }^3{C}_1}{{}^{12}{C}_5}\times \frac{2}{7}$
$=\frac{9\times 8\times 7\times 6\times 120\times 3}{24\times 12\times 11\times 10\times 9\times 8}\times \frac{2}{7}=\frac{3}{22}$