Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done?a)80b)84c)76d)96e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

To form a committee of three members with at least one woman, we can consider two scenarios:

1. When all three members are women
2. When two women and one man are selected

Scenario 1: All three members are women
In this case, we need to select 3 members out of the 5 women available. Since the order of selection doesn't matter, we can use the combination formula.
Number of ways to select 3 women out of 5 = C(5, 3) = (5!)/(3!(5-3)!) = (5!)/(3!2!) = (5 × 4)/(2 × 1) = 10

Scenario 2: Two women and one man are selected
In this case, we need to select 2 women out of the available 5 women and 1 man out of the available 4 men. Again, the order of selection doesn't matter, so we can use the combination formula.
Number of ways to select 2 women out of 5 = C(5, 2) = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 × 4)/(2 × 1) = 10
Number of ways to select 1 man out of 4 = C(4, 1) = (4!)/(1!(4-1)!) = (4!)/(1!3!) = 4

Now, we can calculate the total number of ways to form the committee by adding the possibilities from both scenarios.
Total number of ways = Number of ways in scenario 1 + Number of ways in scenario 2
= 10 + (10 × 4) [since we can choose the man in 4 different ways for each combination of 2 women]
= 10 + 40
= 50

Therefore, the committee can be formed in 50 different ways.

The correct option is A) 80, which is an error in the given answer choices. The correct answer is 50, as explained above.

Similar Quant Doubts

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done if the committee should have all the 4 professors and 1 research associate or all 3 trainees and 2 professors?

There are 6 men and 7 women. In how many ways a committee of 4 members can be made such that a particular man is always to be excluded?

There are 6 men and 7 women. In how many ways a committee of 4 members can be made such that a particular woman is always included.

There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?

There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company