Discussion
The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is
Answer: C
There are 46 ways.
With at least two men and exactly twice as many women, the committee must be either 2 men and 4 women or 3 men and 6 women.
\[ \begin{aligned} \binom{3}{2}\binom{6}{4} &= 3 \times 15 = 45 \\ \binom{3}{3}\binom{6}{6} &= 1 \times 1 = 1 \\ \text{total} &= 45 + 1 = 46 \end{aligned} \]
45 is the first case alone, which forgets the committee of all nine people. A single man with two women is excluded by the condition 'at least two men'.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development