Allied & ICAR Exam Bank • ALLIED_2350 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

A panel of 6 members is to be selected from 6 men and 5 women such that women are in the strict majority. In how many ways can this be done?

Options:

  • (A) 81
  • (B) 96
  • (C) 75
  • (D) 105

Answer Key:

A

Step-by-Step Solution & Explanation

Women majority in a 6-member panel requires $\ge 4$ women. Case 1 (4 women, 2 men): $^5C_4 \times ^6C_2 = 5 \times 15 = 75$. Case 2 (5 women, 1 man): $^5C_5 \times ^6C_1 = 1 \times 6 = 6$. Total ways = $75 + 6 = 81$.
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