Question

Five numbers $x_1,x_2,x_3,x_4,x_5$ are randomly selected from the numbers $1,2,3,\dots \dots ,18$ 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 $1,2,3\dots \dots \dots \dots \dots .18$
$n(s)={}^{18}{C}_5$

$n(E)={}^6{C}_1\times {}^3{C}_1\times {}^7{C}_1$
$P(E)=\frac{6\times 3\times 7}{{}^{18}{C}_5}$
$\frac{1}{17\times 4}=\frac{1}{68}$