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07 Dec 2020, 08:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (02:07) correct
23%
(02:35)
wrong
based on 175
sessions
History
Date
Time
Result
Not Attempted Yet
A committee consisting of 5 members is to be formed out of 6 men and 4 women. How many committees can be formed so that at least one woman is always in the committee?
A. 123
B. 246
C. 252
D. 300
E. 867
A. 123
B. 246
C. 252
D. 300
E. 867
07 Dec 2020, 08:21
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Given: A committee consisting of 5 members is to be formed out of 6 men and 4 women.
Asked: How many committees can be formed so that at least one woman is always in the committee?
Number of committees = 6C4*4C1 + 6C3*4C2 + 6C2*4C3 + 6C1*4C4 = 15*4 + 20*6 + 15*4 + 6*1 = 60 + 120 + 60 + 6 = 246
IMO B
Asked: How many committees can be formed so that at least one woman is always in the committee?
Number of committees = 6C4*4C1 + 6C3*4C2 + 6C2*4C3 + 6C1*4C4 = 15*4 + 20*6 + 15*4 + 6*1 = 60 + 120 + 60 + 6 = 246
IMO B
07 Dec 2020, 08:23
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Given: A committee consisting of 5 members is to be formed out of 6 men and 4 women.
Asked: How many committees can be formed so that at least one woman is always in the committee?
Total number of 5 members committee = 10C5 = 252
Number of 5 members committee with no women = 6C5 = 6
Number of committees can be formed so that at least one woman is always in the committee = 252 - 6 = 246
IMO B
Asked: How many committees can be formed so that at least one woman is always in the committee?
Total number of 5 members committee = 10C5 = 252
Number of 5 members committee with no women = 6C5 = 6
Number of committees can be formed so that at least one woman is always in the committee = 252 - 6 = 246
IMO B
23 Feb 2026, 12:04
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men= 6
women = 4
select total 5 people
we need at least 1 women.
in that scenario we would have to consider 3 different scenario. thats more time consuming.
so we will go the other way and rather select all 5 men and then subtract from overall ways of selecting 5 people from given 10.
so ways to select 5 from 10 = 10C5 = 6*42
now to select 5 men from 6. 6C5= 6
(42*6) - 6
6*41
246
option B
women = 4
select total 5 people
we need at least 1 women.
in that scenario we would have to consider 3 different scenario. thats more time consuming.
so we will go the other way and rather select all 5 men and then subtract from overall ways of selecting 5 people from given 10.
so ways to select 5 from 10 = 10C5 = 6*42
now to select 5 men from 6. 6C5= 6
(42*6) - 6
6*41
246
option B
Bunuel
