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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2022 · Mathematics · Permutation and Combination

A box contains 2 white balls, 3 black balls and 4 red balls. What...

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?

Options

  1. A8484
  2. B7272
  3. C6464
  4. D4848

Correct answer

C. 6464

Step-by-step solution

W=2,B=3,R=4\mathrm{W}=2, \mathrm{ B}=3, \mathrm{R}=4 Total balls =2+3+4=9∴=2+3+4=9\therefore \quad Number of ways of drawing 3 balls with at least one black ball =3C1⋅6C2+3C2⋅6C1+3C3=45+18+1=64\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}
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