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 1 < x 4 < x 2 . The probability that x 2 = 7 and x 4 = 11 is

We know x 1 < 7 < x 3 < 11 < x 5 x 1 ∈ 1 , 2 , 3 , 4 , 5 , 6 x 3 ∈ 8 , 9 , 10 x 5 ∈ 12 , 13 , 14 , 15 , 16 , 17 , 18 Required probability P = C 1 6 × C 1 3 × C 1 7 C 5 18 = 1 68

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MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Hard2 minPYQ_2022

MathematicsHardsingle choice

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 $(x_{1} < x_{2} < x_{1} < x_{4} < x_{2})$ . The probability that $x_{2} = 7$ and $x_{4} = 11$ is

Options:

Answer:

Solution:

We know $x_{1} < 7 < x_{3} < 11 < x_{5}$

$x_{1} \in \{1, 2, 3, 4, 5, 6\}$

$x_{3} \in \{8, 9, 10\}$

$x_{5} \in \{12, 13, 14, 15, 16, 17, 18\}$

Required probability $P = \frac{{}^{6}C_{1} \times {}^{3}C_{1} \times {}^{7}C_{1}}{{}^{18}C_{5}} = \frac{1}{68}$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: PYQ_2022

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