Q261 / 270 · NDA 2022 (Phase 2) · Mathematics

A box contains 2 white balls, 3 black balls and 4 red balls. What is the number of ways of drawing 3 balls from the box with at least one black ball?

  • A
    $84$
  • B
    $72$
  • Correct answer
    C
    $64$
  • D
    $48$

Solution

$\mathrm{W}=2, \mathrm{~B}=3, \mathrm{R}=4$ Total balls $=2+3+4=9$ $\therefore \quad$ Number of ways of drawing 3 balls with at least one black ball $\begin{aligned} & ={ }^3 C_1 \cdot{ }^6 C_2+{ }^3 C_2 \cdot{ }^6 C_1+{ }^3 C_3 \\ & =45+18+1=64 \end{aligned}$

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

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