Combinations
From a group of 7 men and 4 women, a committee of 5 persons is to be formed. In how many ways can this be done if the committee must have at least 2 women?
Select the correct option:
Solution
301
- Identify Cases: Since there are 4 women available, 'at least 2' means 2, 3, or 4 women.
- Calculate Each Case:
- Case 1 (2W, 3M): C(4,2)×C(7,3)=6×35=210.
- Case 2 (3W, 2M): C(4,3)×C(7,2)=4×21=84.
- Case 3 (4W, 1M): C(4,4)×C(7,1)=1×7=7.
- Sum the Mutually Exclusive Events:
- Total = 210+84+7=301.
- Verification: Note that we cannot have 5 women because only 4 exist.
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- combinations
- Difficulty
- Hard
- Year
- 2025
This hard difficulty mathematics question is from the chapter permutations and combinations, covering the topic of combinations. It appeared in the 2025 exam. Practice this and similar questions to strengthen your understanding of permutations and combinations concepts.
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