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Bunuel
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How many different committees can be formed from a group of two women 10 Jun 2016, 01:01
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (01:24) correct 27% (01:43) wrong based on 325 sessions

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How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?

A. 6
B. 8
C. 10
D. 12
E. 16
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E
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How many different committees can be formed from a group of two women 10 Jun 2016, 02:10
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Bunuel
How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?

A. 6
B. 8
C. 10
D. 12
E. 16
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2 Women and 4 Men. Three people needed
It is always better to subtract the total from none in case of at least one problems.

Total ways = 6C3 = 20
Total ways without any women = 4C3 = 4

Hence ways in which at least one women will be present = 20 - 4 = 16

Correct option: E
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How many different committees can be formed from a group of two women 10 Jun 2016, 01:14
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2C1*4C2 + 2C2*4C1 = 16 E is the answer.
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How many different committees can be formed from a group of two women 10 Jun 2016, 09:27
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E-16

2C1*4C2 + 2C2* 4C1 =12+4 =16

very easy method
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How many different committees can be formed from a group of two women 10 Jun 2016, 09:38
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We have 2 women = 2 W, and 4 men = 4M

We want to select 3 people from these 2W and 4M, with at least 1 W

So we can have : WMM or WWM, but no more women since there are only 2.

WMM = 1 from 2 * 2 from 4 = 12
WWM = 2 from 2 * 1 from 4 = 4

So, 12 + 4 = 16
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How many different committees can be formed from a group of two women 30 Aug 2021, 06:13
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Solution

s

Given
    • Group of two women and four men.

To find
    • Committee of three people such that at least one member must be a woman.

Approach and Working out
Total number of ways of selecting three people out of 4 men and 2 women = \(6C_3\) = 20.
The number of ways of selecting three people with no woman = \(4C_3\) = 4.

Thus, the number of ways of selecting 3 people out of two groups such that at least one woman is selected = 20 = 4 = 16.

Correct Answer: Option E
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How many different committees can be formed from a group of two women 28 Oct 2025, 08:29
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