Question

Five numbers $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ are randomly selected from the numbers $1,2,3, \ldots \ldots, 18$ and are arranged in the increasing order $\left(x_{1}< x_{2}< x_{3}< x_{4}< x_{5}\right)$. The probability that $x _{2}=7$ and $x _{4}=11$ is :

• A. $\frac{1}{136}$
• B. $\frac{1}{72}$
• C. $\frac{1}{68}$
• D. $\frac{1}{34}$

Answer 1

Answer: (C)

No. of ways to select and arrange $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$
from $1,2,3 \ldots \ldots \ldots \ldots \ldots .18$
$n ( s )={ }^{18} C _{5}$

$n ( E )={ }^{6} C _{1} \times{ }^{3} C _{1} \times{ }^{7} C _{1}$
$P(E)=\frac{6 \times 3 \times 7}{{ }^{18} C_{5}}$
$\frac{1}{17 \times 4}=\frac{1}{68}$