Q107 / 155 · WBJEE 2025 · Mathematics

Three numbers are chosen at random without replacement from $\{1,2, \ldots .10\}$. The probability that the minimum of the chosen numbers is 3 or their maximum is 7 , is

  • A
    $\frac{5}{40}$
  • B
    $\frac{3}{40}$
  • Correct answer
    C
    $\frac{11}{40}$
  • D
    $\frac{9}{40}$

Solution

$\frac{{ }^7 \mathrm{C}_2+{ }^6 \mathrm{C}_2-{ }^3 \mathrm{C}_1}{{ }^{10} \mathrm{C}_3}=\frac{33}{120}=\frac{11}{40}$

Hence, the correct answer is option: 'C'.

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