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JEE Main 202227 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2022 · 27 June · Morning Shift · Mathematics · Probability

Five numbers x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 are randomly...

Five numbers x1,x2,x3,x4,x5{x}_{1}, {x}_{2}, {x}_{3}, {x}_{4}, {x}_{5} are randomly selected from the numbers1,2,3,……,181, 2, 3, \ldots \ldots , 18 and are arranged in the increasing order \left({x}_{1} < {x}_{2} < {x}_{1} < {x}_{4} < {x}_{2}\right).Theprobabilitythat. The probability that{x}_{2} = 7 and {x}_{4} = 11 is

Options

  1. A1136\dfrac{1}{136}
  2. B168\dfrac{1}{68}
  3. C768\dfrac{7}{68}
  4. D568\dfrac{5}{68}

Correct answer

B. 168\dfrac{1}{68}

Step-by-step solution

We know x1<7<x3<11<x5{x}_{1} < 7 < {x}_{3} < 11 < {x}_{5}

x1∈{1,2,3,4,5,6}{x}_{1} \in \left\{1, 2, 3, 4, 5, 6\right\}

x3∈{8,9,10}{x}_{3} \in \left\{8, 9, 10\right\}

x5∈{12,13,14,15,16,17,18}{x}_{5} \in \left\{12, 13, 14, 15, 16, 17, 18\right\}

Required probability P=C16×C13×C17C518=168P = \dfrac{C1 6 \times C1 3 \times C1 7}{C5 18} = \dfrac{1}{68}

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