Five numbers x _{1}, x _{2}, x _{3}, x _{4}, x _{5} are randomly selected from numbers 1,2,3, ldots

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14.Probability

hard

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

$\frac{1}{68}$

C

$\frac{1}{72}$

D

$\frac{1}{34}$

(JEE MAIN-2022)

Solution

No. of ways to select and arrange $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ from $1,2,3 \ldots \ldots \ldots \ldots \ldots . \ldots18$

$n ( s )={ }^{18} C _{5}$

$x_{1}\left (x_{2}\right) \quad x_{3} \quad\left(x_{4}\right)\quad x_{5}$

$7$ $11$

$n ( E )={ }^{6} C _{1} \times{ }^{3} C _{1} \times{ }^{7} C _{1}$

$P(E)=\frac{6 \times 3 \times 7}{{ }^{18} C_{5}}$

$\frac{1}{17 \times 4}=\frac{1}{68}$

Standard 11

Mathematics

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