Question

Five numbers, $x_1, x_2, x_3, x_4, x_5$ are randomly selected from the numbers $1, 2, 3$,….., $18$ and are arranged in the increasing order $(x_1<x_2<x_3<x_4<x_5)$. 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)

$\frac{1}{68}$

Answer 2

The number of Total cases

=$^{18}C_5$

Favourable cases

$^6C_1$ $^3C_1$ $^7C_1$

$(Select \;x_1)$ $(Select \;x_3)$ $(Select \;x_5)$

$P =\frac{ 6.3.7}{^{18}C_5}$

= $\frac{1}{68}$

Hence, the correct option is (C): $\frac{1}{68}$