Allied & ICAR Exam Bank • ALLIED_1714 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

A box contains 5 red, 4 green, and 3 blue balls. In how many ways can 3 balls be drawn such that at least one green ball is included?

Options:

  • (A) 164
  • (B) 140
  • (C) 180
  • (D) 120

Answer Key:

A

Step-by-Step Solution & Explanation

Total ways to choose 3 from 12 = $^{12}C_3 = \frac{12 \times 11 \times 10}{6} = 220$. Ways with no green ball (from $5+3=8$ balls) = $^8C_3 = 56$. At least one green = $220 - 56 = 164$.
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