Question

Suppose $n$ people are asked a question successively in a random order and exactly $3$ of the $n$ people know that answer. If $n>6$, the probability that the first four of those asked do not know the answer is

• A. $\frac{{}^{n-4}{C}_4}{{}^n{C}_4}$
• B. $\frac{{}^{n-3}{C}_4}{{}^n{C}_4}$
• C. $\frac{1}{{}^n{C}_4}$
• D. None of these

Answer 1

Answer: (B)

$\frac{{}^{n-3}{C}_4}{{}^n{C}_4}$

Out of $n$ people, $3$ know the answer and $(n-3)$ do not know the answer.
The first four persons will not know the answer is that they are chosen out of the $(n-3)$ people who do not know the answer.
Thus, the probability of the required event is $\frac{{}^{n-3}{C}_4}{{}^n{C}_4}$.