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23 Dec 2024, 11:19
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B
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Difficulty:
35%
(medium)
Question Stats:
76% (02:26) correct
24%
(02:32)
wrong
based on 76
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A committee of 6 members is to be selected from a group of 10 people, consisting of 4 men and 6 women. How many different committees can be formed if the committee must have at least 3 women?
A. 183
B. 195
C. 194
D. 184
E. 204
A. 183
B. 195
C. 194
D. 184
E. 204
23 Dec 2024, 11:34
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At least 3 women - 4 cases => 3 women 3 men, or 4 women 2 men, or 5 women 1 men, or 6 women
6C3 4C3 + 6C4 4C2 + 6C5 4C1 + 6C6 = 80 + 90 + 24 + 1 = 195
Answer B.
6C3 4C3 + 6C4 4C2 + 6C5 4C1 + 6C6 = 80 + 90 + 24 + 1 = 195
Answer B.
24 Dec 2024, 14:18
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HarshaBujji
A committee of 6 members is to be selected from a group of 10 people, consisting of 4 men and 6 women. How many different committees can be formed if the committee must have at least 3 women?
A. 183
B. 195
C. 194
D. 184
E. 204
Committees with atleast 3 women can also be interpreted as subtracting committees having zero, one or two women from total committees of 6 people.A. 183
B. 195
C. 194
D. 184
E. 204
Another interesting observation by looking at the numbers here is that, you cannot form a committee with less than 2 women, as we only have 4 men. So you will need to select atleast 2 women to form a committee of 6 people => This simplifies our calculation a lot.
Required combinations = Total combinations to select a committee of 6 people - Number of combinations where committee has exactly 2 women
10C6 - 6C2*4C4
10C4 - 6C2
210 - 15
195
Answer: B
