JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q16

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MathematicsSingle correct+4 / -1Question 16 of 90

Five numbers $x_1,x_2,x_3,x_4,x_5$ are randomly selected from the numbers $1,2,3,\dots,18$ 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 :

\dfrac1{136}

\dfrac1{72}

\dfrac1{68}

\dfrac1{34}

Answer and worked solution

Official answer: C

Favourable. $x_1\in\{1,\dots,6\}$ , $x_3\in\{8,9,10\}$ , $x_5\in\{12,\dots,18\}$ : $6\times3\times7=126$ .

Probability. $\dfrac{126}{\binom{18}5}=\dfrac{126}{8568}=\dfrac1{68}$ .

(C)

Topics:Classical probability Combinations

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JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 16