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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
  • a)
    624
  • b)
    702
  • c)
    756
  • d)
    812
Correct answer is option 'C'. Can you explain this answer?

Ref: https://edurev.in/question/471148/From-a-group-of-7-men-and-6-women-five-persons-are-to-be-selected-to-form-a-committee-so-that-at-le

From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.

Hence we have the following 3 choices

We can select 5 men ------(Option 1)

Number of ways to do this = 7C5

We can select 4 men and 1 woman ------(Option 2) 

Number of ways to do this = 7C4 x 6C1

We can select 3 men and 2 women ------(Option 3) 

Number of ways to do this = 7C3 x 6C2 

Total number of ways 

= 7C5 + [7C4 x 6C1] + [7C3 x 6C2]
= 7C2 + [7C3 x 6C1] + [7C3 x 6C2] [Applied the formula nCr = nC(n - r) ]

=[7×62×1]+[(7×6×53×2×1)×6]+[(7×6×53×2×1)×(6×52×1)]=[7×62×1]+[(7×6×53×2×1)×6]+[(7×6×53×2×1)×(6×52×1)]

= 21 + 210 + 525 = 756

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1. What is the CAT exam?
Ans. The CAT exam, also known as the Common Admission Test, is a national level entrance exam conducted in India for admission to postgraduate management programs offered by various prestigious business schools.
2. What is the eligibility criteria for the CAT exam?
Ans. To be eligible for the CAT exam, a candidate must hold a bachelor's degree with at least 50% marks (45% for SC/ST/PwD candidates) or equivalent CGPA from a recognized university. Final year students are also eligible to apply.
3. How can I apply for the CAT exam?
Ans. To apply for the CAT exam, candidates need to visit the official website and register online. The registration process typically starts in August and requires filling out personal details, educational qualifications, selecting exam centers, and paying the application fee.
4. What is the exam pattern of the CAT exam?
Ans. The CAT exam consists of three sections: Verbal Ability and Reading Comprehension (VARC), Data Interpretation and Logical Reasoning (DILR), and Quantitative Ability (QA). The total duration of the exam is 2 hours and includes both multiple-choice questions and non-multiple-choice questions.
5. How is the CAT exam scored?
Ans. The CAT exam is scored on a percentile basis. Each section is given a scaled score ranging from 0 to 100, and the overall percentile score is calculated based on the candidate's performance compared to other test-takers. The final percentile score determines the candidate's rank and eligibility for admission to various management programs.
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