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 :
Solution
No. of ways to select and arrange $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4, \mathrm{x}_5$ from $1,2,3$.......18<br/><br/>
$$
\begin{aligned}
& \mathrm{n}(\mathrm{s})={ }^{18} \mathrm{C}_5 \\\\
& \begin{array}{lllll}
x_1 & \underset{7}{\left(x_2\right)} & x_3 & \underset{11}{\left(x_4\right)} & x_5
\end{array} \\\\
& \mathrm{n}(\mathrm{E})={ }^6 \mathrm{C}_1 \times{ }^3 \mathrm{C}_1 \times{ }^7 \mathrm{C}_1 \\\\
& P(E)=\frac{6 \times 3 \times 7}{{ }^{18} C_5} \\\\
& \frac{1}{17 \times 4}=\frac{1}{68} \\\\
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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