Question

A bag contains 50 tickets numbered 1, 2, 3, ..., 50 of which five are drawn at random and arranged in ascending order of magnitude $(x_1<x_2<x_3<x_4<x_5)$. The probability that $x_3=30$ is

• A. $\frac{{}^{20}{C}_2}{{}^{50}{C}_5}$
• B. $\frac{{}^{29}{C}_2}{{}^{50}{C}_5}$
• C. $\frac{{}^{20}{C}_2{\times }^{29}{C}_2}{{}^{50}{C}_5}$
• D. None of these

Answer 1

Answer: (C)

$\frac{{}^{20}{C}_2{\times }^{29}{C}_2}{{}^{50}{C}_5}$

First and second number should be from tickets numbered $1$ to $29{=}^{29}{C}_2$ ways and remaining two in ${}^{20}{C}_2$ ways
Therefore, favorable number of events
${=}^{29}{C}_2{\times }^{20}{C}_2$
$\therefore$Required probability$=\frac{{}^{29}{C}_2{\times }^{20}{C}_2}{{}^{50}{C}_5}$